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</results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="16.97953" top="70.86614" bottom="70.86614"/> <header use-full-page-width="true"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs16\{p\}\par \{f\}\par \par } </left> </header> <footer use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset0 Arial;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\lang1033\f0\fs16\{d\}\cf0\lang1049\f1\fs18\par }</left> <center>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial 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</calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1297" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1090" left="30" top="12.75" width="472.5" height="122.25" align-x="30" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Шаблон решения РК2.<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal">Вариант 12.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">Решить численно</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> дифференциальное уравнение 2-го порядка<sp count="2"/> </f> <region region-id="1088" left="375.75" top="27.75" width="90" height="44.25" align-x="410.25" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">методом припасовывания</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>где функция f(x,y,y1) может быть задана выражением:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1087" left="33" top="108" width="183" height="15.75" align-x="87" align-y="119.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">kk</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Здесь </inlineAttr> </f> <region region-id="1221" left="259.5" top="98.25" width="61.5" height="36.75" align-x="278.25" align-y="119.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </math> <rendering item-idref="4"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="1236" left="36" top="156" width="31.5" height="14.25" align-x="36" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Дано: </f> </text> </region> <region region-id="1235" left="96" top="156.75" width="27.75" height="15.75" align-x="108.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="5"/> </region> <region region-id="1234" left="156" top="151.5" width="33" height="21" align-x="169.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <region region-id="1241" left="234" top="156.75" width="27.75" height="15.75" align-x="246.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">c</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="7"/> </region> <region region-id="1240" left="288" top="156.75" width="34.5" height="15.75" align-x="307.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">kk</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="8"/> </region> <region region-id="1242" left="36" top="193.5" width="175.5" height="21" align-x="90.75" align-y="210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>-0</ml:real> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1250" left="312" top="195" width="90.75" height="36.75" align-x="386.25" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="10"/> </region> <region region-id="1103" left="30" top="240.75" width="168.75" height="13.5" align-x="30" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">1-я и 2-я производные заданы:</f> </text> </region> <region region-id="1104" left="210" top="240.75" width="87.75" height="15.75" align-x="276" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">U1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">y1</ml:id> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1105" left="312" top="240.75" width="123" height="15.75" align-x="378" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">U2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="967" left="36" top="264.75" width="93.75" height="13.5" align-x="36" align-y="276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3-я производная:</f> </text> </region> <region region-id="962" left="30" top="291" width="368.25" height="36.75" align-x="96" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="dd62d7d7-9936-4965-89ae-cf836ae1798f" version-id="2c719afe-b9ac-40b7-be83-90a59691541e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="17" is-modified="true" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\МетПрипасовывания.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef 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xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="13"> <element-image-map> <box left="1.5" top="0.75" width="366.75" height="35.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="963" left="36" top="336.75" width="93.75" height="13.5" align-x="36" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4-я производная:</f> </text> </region> <region region-id="1124" left="36" top="363.75" width="442.5" height="240.75" align-x="102" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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<ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">y1</ml:id> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1150" left="30" top="648.75" width="467.25" height="13.5" align-x="30" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим начальные условия </f> </text> </region> <region region-id="1263" left="30" top="678.75" width="35.25" height="17.25" align-x="48.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1264" left="90" top="678.75" width="35.25" height="17.25" align-x="108.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1265" left="144" top="678.75" width="41.25" height="17.25" align-x="168.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1269" left="30" top="726" width="443.25" height="41.25" align-x="30" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Интервал по </f> <f family="Arial Cyr" charset="204" size="12"> x </f> <f family="Arial Cyr" charset="204" size="12"> может быть непосредственно связан с проблемой сингулярности. </f> <f family="Arial Cyr" charset="204" size="12">Поэтому следует указать особые точки и исключить их из области определения</f> <f family="Arial Cyr" charset="204" size="12">искомого решения. Особое внимание уделить нелинейным уравнениям.</f> </text> </region> <region region-id="1291" left="36" top="774.75" width="90.75" height="13.5" align-x="36" align-y="786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">И дискрет по "x":</f> </text> </region> <region region-id="1260" left="30" top="816.75" width="36.75" height="15.75" align-x="50.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">bb</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1261" left="102" top="808.5" width="94.5" height="33.75" align-x="115.5" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:minus/> <ml:real>0.8</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">FRAME</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1262" left="234" top="807" width="101.25" height="35.25" align-x="251.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">bb</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1247" left="30" top="858.75" width="38.25" height="15.75" align-x="46.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="1246" left="102" top="858.75" width="49.5" height="15.75" align-x="116.25" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1245" left="186" top="858.75" width="68.25" height="17.25" align-x="204.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1244" left="288" top="858.75" width="41.25" height="17.25" align-x="307.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="1248" left="372" top="858.75" width="39.75" height="17.25" align-x="390" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="1110" left="24" top="894.75" width="478.5" height="27" align-x="24" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Если Вы хотите сравнить полученное Вами решение с ответом, откройте в электрон-</f> <f family="Arial Cyr" charset="204" size="12">ной версии пособия ниже представленную закрытую область.</f> </text> </region> <region region-id="1156" left="0" top="957" width="6008.25" align-x="8.25" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="740.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" 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z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.59934784853333356</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="978" left="390" top="1356.75" width="68.25" height="17.25" align-x="409.5" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6.7815862866934609</ml:real> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="979" left="480" top="1356.75" width="21" height="13.5" align-x="480" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial" charset="0" size="12">OK!</f> </text> </region> <region region-id="1270" left="54" top="1512" width="276" height="141.75" align-x="54" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="37"/> <rendering item-idref="38"/> </region> </area> <rendering item-idref="39"/> </region> <region region-id="1177" left="24" top="1722.75" width="66" height="15.75" align-x="73.5" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1178" left="24" top="1752.75" width="495" height="39" align-x="24" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Параметры дифференциального уравнения и их условные обозначения взяты из </f> <f family="Arial Cyr" charset="204" size="12">таблицы РК 2 (выписать только числовые данные со </f> <f family="Arial Cyr" charset="204" size="12">знаком присвоения и функции).</f> <f family="Arial Cyr" charset="204" size="10"> Примечание </f> <f family="Arial Cyr" charset="204" size="10">. Все имена должны быть уникальными.</f> </text> </region> <region region-id="1289" left="36" top="1818.75" width="30" height="15.75" align-x="49.5" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1288" left="96" top="1813.5" width="35.25" height="21" align-x="110.25" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> 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пример задания Bulstoer.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">76edc7c2a81527b19a5c9faff6d701aa</contentHash> <ml:define> <ml:id xml:space="preserve">y0</ml:id> <ml:real>1</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="45"> <element-image-map> <box left="1.5" top="0.75" width="34.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1284" left="366" top="1818.75" width="41.25" height="15.75" align-x="390.75" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">yy1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="1280" left="36" top="1848.75" width="93" height="15.75" align-x="66.75" align-y="1860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">ff</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">kk</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="1281" left="144" top="1842.75" width="141.75" height="21.75" align-x="180.75" align-y="1860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve">ff</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="1" cols="6"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="1186" left="30" top="1878.75" width="465.75" height="33" align-x="30" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Запись оператора D(x,z), задающего<sp count="2"/>правые части системы дифференциальных уравнений (здесь z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y,<sp count="2"/>z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y</f> <f family="Arial Cyr" charset="204" size="12">'</f> <f family="Arial Cyr" charset="204" size="12">), эквивалентной уравнению y</f> <f family="Arial Cyr" charset="204" size="12"> '' </f> <f family="Arial Cyr" charset="204" size="12">+ a*y</f> <f family="Arial Cyr" charset="204" size="12"> ' </f> <f family="Arial Cyr" charset="204" size="12">+ b*y = f(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1187" left="42" top="1944.75" width="160.5" height="39.75" align-x="83.25" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ff</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:matrix> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="1297" left="294" top="1942.5" width="168" height="45" align-x="336" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">D</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>-0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ff</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="1189" left="30" top="2016.75" width="453.75" height="27.75" align-x="30" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вектор начальных условий, число точек отсчёта, начало и конец интервала незави-</f> <f family="Arial Cyr" charset="204" size="12">симой переменной </f> <f family="Arial Cyr" charset="204" size="12"> х </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="1190" left="54" top="2066.25" width="60" height="36.75" align-x="70.5" align-y="2088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V</ml:id> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">yy1</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="1191" left="144" top="2076.75" width="45.75" height="15.75" align-x="161.25" align-y="2088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef 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show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">xk</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="1194" left="48" top="2118.75" width="453" height="13.5" align-x="48" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение теперь уже системы дифференциальных уравнений:</f> </text> </region> <region region-id="1195" left="48" top="2154.75" width="145.5" height="15.75" align-x="63.75" align-y="2166" show-border="false" show-highlight="false" 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font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3" imaginary-value="i" zero-threshold="15"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="16.97953" top="70.86614" bottom="70.86614"/> <header use-full-page-width="true"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs16\{p\}\par \{f\}\par \par } </left> </header> <footer use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset0 Arial;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\lang1033\f0\fs16\{d\}\cf0\lang1049\f1\fs18\par }</left> <center>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\qc\f0\fs18\'d2\'e8\'f2\'ee\'e2\par }</center> <right>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset204{\*\fname Arial;}Arial CYR;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\qr\cf1\f0\fs16\{n\}\cf0\f1\fs18\par }</right> </footer> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="EN" UI="EN"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1297" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1090" left="30" top="12.75" width="472.5" height="122.25" align-x="30" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Шаблон решения РК2.<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal">Вариант 12.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">Решить численно</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> дифференциальное уравнение 2-го порядка<sp count="2"/> </f> <region region-id="1088" left="375.75" top="27.75" width="90" height="44.25" align-x="410.25" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">методом припасовывания</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>где функция f(x,y,y1) может быть задана выражением:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1087" left="33" top="108" width="183" height="15.75" align-x="87" align-y="119.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">kk</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Здесь </inlineAttr> </f> <region region-id="1221" left="259.5" top="98.25" width="61.5" height="36.75" align-x="278.25" align-y="119.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </math> <rendering item-idref="4"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="1236" left="36" top="156" width="31.5" height="14.25" align-x="36" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Дано: </f> </text> </region> <region region-id="1235" left="96" top="156.75" width="27.75" height="15.75" align-x="108.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="5"/> </region> <region region-id="1234" left="156" top="151.5" width="33" height="21" align-x="169.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <region region-id="1241" left="234" top="156.75" width="27.75" height="15.75" align-x="246.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">c</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="7"/> </region> <region region-id="1240" left="288" top="156.75" width="34.5" height="15.75" align-x="307.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">kk</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="8"/> </region> <region region-id="1242" left="36" top="193.5" width="175.5" height="21" align-x="90.75" align-y="210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>-0</ml:real> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1250" left="312" top="195" width="90.75" height="36.75" align-x="386.25" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="10"/> </region> <region region-id="1103" left="30" top="240.75" width="168.75" height="13.5" align-x="30" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">1-я и 2-я производные заданы:</f> </text> </region> <region region-id="1104" left="210" top="240.75" width="87.75" height="15.75" align-x="276" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">U1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">y1</ml:id> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1105" left="312" top="240.75" width="123" height="15.75" align-x="378" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">U2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="967" left="36" top="264.75" width="93.75" height="13.5" align-x="36" align-y="276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3-я производная:</f> </text> </region> <region region-id="962" left="30" top="291" width="368.25" height="36.75" align-x="96" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="dd62d7d7-9936-4965-89ae-cf836ae1798f" version-id="2c719afe-b9ac-40b7-be83-90a59691541e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="17" is-modified="true" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\МетПрипасовывания.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef 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xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="13"> <element-image-map> <box left="1.5" top="0.75" width="366.75" height="35.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="963" left="36" top="336.75" width="93.75" height="13.5" align-x="36" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4-я производная:</f> </text> </region> <region region-id="1124" left="36" top="363.75" width="442.5" height="240.75" align-x="102" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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<ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">y1</ml:id> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1150" left="30" top="648.75" width="467.25" height="13.5" align-x="30" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим начальные условия </f> </text> </region> <region region-id="1263" left="30" top="678.75" width="35.25" height="17.25" align-x="48.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1264" left="90" top="678.75" width="35.25" height="17.25" align-x="108.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1265" left="144" top="678.75" width="41.25" height="17.25" align-x="168.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1269" left="30" top="726" width="443.25" height="41.25" align-x="30" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Интервал по </f> <f family="Arial Cyr" charset="204" size="12"> x </f> <f family="Arial Cyr" charset="204" size="12"> может быть непосредственно связан с проблемой сингулярности. </f> <f family="Arial Cyr" charset="204" size="12">Поэтому следует указать особые точки и исключить их из области определения</f> <f family="Arial Cyr" charset="204" size="12">искомого решения. Особое внимание уделить нелинейным уравнениям.</f> </text> </region> <region region-id="1291" left="36" top="774.75" width="90.75" height="13.5" align-x="36" align-y="786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">И дискрет по "x":</f> </text> </region> <region region-id="1260" left="30" top="816.75" width="36.75" height="15.75" align-x="50.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">bb</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1261" left="102" top="808.5" width="94.5" height="33.75" align-x="115.5" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:minus/> <ml:real>0.8</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">FRAME</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1262" left="234" top="807" width="101.25" height="35.25" align-x="251.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">bb</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1247" left="30" top="858.75" width="38.25" height="15.75" align-x="46.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="1246" left="102" top="858.75" width="49.5" height="15.75" align-x="116.25" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1245" left="186" top="858.75" width="68.25" height="17.25" align-x="204.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1244" left="288" top="858.75" width="41.25" height="17.25" align-x="307.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="1248" left="372" top="858.75" width="39.75" height="17.25" align-x="390" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="1110" left="24" top="894.75" width="478.5" height="27" align-x="24" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Если Вы хотите сравнить полученное Вами решение с ответом, откройте в электрон-</f> <f family="Arial Cyr" charset="204" size="12">ной версии пособия ниже представленную закрытую область.</f> </text> </region> <region region-id="1156" left="0" top="957" width="6008.25" align-x="8.25" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="740.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" 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disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1178" left="24" top="1752.75" width="495" height="39" align-x="24" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Параметры дифференциального уравнения и их условные обозначения взяты из </f> <f family="Arial Cyr" charset="204" size="12">таблицы РК 2 (выписать только числовые данные со </f> <f family="Arial Cyr" charset="204" size="12">знаком присвоения и функции).</f> <f family="Arial Cyr" charset="204" size="10"> Примечание </f> <f family="Arial Cyr" charset="204" size="10">. 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size="12">Запись оператора D(x,z), задающего<sp count="2"/>правые части системы дифференциальных уравнений (здесь z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y,<sp count="2"/>z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y</f> <f family="Arial Cyr" charset="204" size="12">'</f> <f family="Arial Cyr" charset="204" size="12">), эквивалентной уравнению y</f> <f family="Arial Cyr" charset="204" size="12"> '' </f> <f family="Arial Cyr" charset="204" size="12">+ a*y</f> <f family="Arial Cyr" charset="204" size="12"> ' </f> <f family="Arial Cyr" charset="204" size="12">+ b*y = f(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1187" left="42" top="1944.75" width="160.5" height="39.75" align-x="83.25" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">D</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ff</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:matrix> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="1297" left="294" top="1942.5" width="168" height="45" align-x="336" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">D</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>-0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ff</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="1189" left="30" top="2016.75" width="453.75" height="27.75" align-x="30" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вектор начальных условий, число точек отсчёта, начало и конец интервала незави-</f> <f family="Arial Cyr" charset="204" size="12">симой переменной </f> <f family="Arial Cyr" charset="204" size="12"> х </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="1190" left="54" top="2066.25" width="60" height="36.75" align-x="70.5" align-y="2088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V</ml:id> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">yy1</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="1191" left="144" top="2076.75" width="45.75" height="15.75" align-x="161.25" align-y="2088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef 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show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">xk</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="1194" left="48" top="2118.75" width="453" height="13.5" align-x="48" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение теперь уже системы дифференциальных уравнений:</f> </text> </region> <region region-id="1195" left="48" top="2154.75" width="145.5" height="15.75" align-x="63.75" align-y="2166" show-border="false" show-highlight="false" 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