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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xt0G6$/-%\"xG6 #\"\"!F*/--%\"DG6#F(F)F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "\315 \340\365\356\344\350\354 \360\345\370\345\355\350\345:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "dsolve(\{de,xt0\},x(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"xG6#%\"tG,(*.-%$sinG6#*&%\"KG\"\"\"F'F/ F/F.!\"\",&*$)F.\"\"#F/F/*$)%&omegaGF4F/F0F0%\"hGF/-%$cosG6#%&deltaGF/ F7F/F/**-F:F,F/F8F/-F+F;F/F1F0F/*(F8F/-F+6#,&*&F7F/F'F/F/F " 0 "" {MPLTEXT 1 0 173 "sys:=diff(y(x),x) =2*z(x)-y(x)-x, diff(z(x),x)=y(x); \+ fns:=\{y(x),z(x)\}; yx0:=y(0)=0,z(0)=1; dsol ve(\{sys,yx0\},fns);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sysG6$/-%%d iffG6$-%\"yG6#%\"xGF-,(*&\"\"#\"\"\"-%\"zGF,F1F1F*!\"\"F-F4/-F(6$F2F-F *" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$fnsG<$-%\"yG6#%\"xG-%\"zGF(" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yx0G6$/-%\"yG6#\"\"!F*/-%\"zGF)\" \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"yG6#%\"xG,(*&#\"\"\"\" \"$F,-%$expGF'F,F,*&#\"\"&\"\"'F,-F/6#,$*&\"\"#F,F(F,!\"\"F,F9#F,F8F,/ -%\"zGF',**&F+F,F.F,F,*&#F2\"#7F,F4F,F,#F,\"\"%F,*&F8F9F(F,F," }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "\315\340\365\356\344\350\354 \360 \345\370\345\355\350\345, \357\360\345\344\361\362\340\342\353\377\345 \354\356\345 \360\377\344\356\354: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Order:=6: dsolve(\{sys,yx0\},fns,series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"yG6#%\"xG+/F(\"\"#\"\"\"#!\"$F*F*#\" \"(\"\"'\"\"$#!#8\"#C\"\"%#\"\"*\"#S\"\"&-%\"OG6#F+F0/-%\"zGF'+/F(F+\" \"!F+F*#!\"\"F*F1#F/F4F5#F3\"$?\"F9F:F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "\310\361\357\356\353\374\347\363\345\354 \356\357\345\360 \340\362\356\360\355\373\351 \354\345\362\356\344 \355\340\365\356\346 \344\345\355\350\377 \360\345\370\345\355\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sol := dsolve(\{sys, yx0\}, fns, method=lap lace);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<$/-%\"yG6#%\"xG,(*&# 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" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "------------ \312 \360\345 \370\345\355\350\376 \347\340\344\340\367 \354\345\362\356\344\356\354 \335\351\353\345\360\340 -------------------------------------------- ------" }}{PARA 0 "" 0 "" {TEXT -1 71 "\361\354. \362\340\352\346\345 \+ \324\340\351\353: \"....\\Ps_\314\303\322\323\\\313\340\341\356\360 \340\362\356\360\355\373\345 \360\340\341\356\362\373 \357\356 \367 \350\361\353\345\355\355\373\354 \354\345\362\356\344\340\354\\" }} {PARA 0 "" 0 "" {TEXT -1 69 "\322\356\353\374\352\356 \344\353\377 \+ \354\345\355\377 \316\362\342\345\362\373\\\323\357\360\340\346\355 \315\340_\314\345\362\356\344\335\351\353\345\360\340.mws\" \322\350 \362\356\342 \312.\302. 03.03.14." }}{PARA 0 "" 0 "" {TEXT -1 15 "\312 \356\360. 09.03.17. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "res tart; with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "\327\350 \361\353\345\355\355\356\345 \360\345\370\345\355\350\345 \304\323 1- \343\356 \357\356\360\377\344\352\340, \350\354\345\376\371\345\343 \356 \357\360\340\342\363\376 \367\340\361\362\374 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=t->cos(y(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"tG6\"6$%)operatorG%&arrowGF(-%$cosG6#-%\"y G6#9$F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "\322\345\357\345 \360\374 \347\340\357\350\370\345\354 \355\340\367\340\353\374\355\373 \345 \363\361\353\356\342\350\377 \342 \362\356\367\352\345 t0 \357 \356\344 \350\354\345\355\345\354 yt0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "yt0:=y(0)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yt 0G/-%\"yG6#\"\"!F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "\307\340 \357\350\370\345\354 \360\345\370\340\345\354\356\345 \304\323" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "de:=diff(y(t),t$1)=f(t);" } {TEXT -1 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#deG/-%%diffG6$-%\" yG6#%\"tGF,-%$cosG6#F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "\321 \356\361\362\340\342\350\354 \347\340\344\340\355\350\345 \355\340 \+ \360\345\370\345\355\350\345 \344\350\364\364\345\360\345\355\366\350 \340\353\374\355\356\343\356 \363\360\340\342\355\345\355\350\377." }} {PARA 0 "" 0 "" {TEXT 273 1 "1" }{TEXT -1 24 ". \300\355\340\353\350 \362\350\367\345\361\352\356\345 \360\345\370\345\355\350\345:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "resh:=dsolve(\{de,yt0\},y(t) ); rhs(resh);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%reshG/-%\"yG6#%\"t G-%'arctanG6$*&,&*$)-%$expGF(\"\"#\"\"\"F4F4!\"\"F4,&F/F4F4F4F5,$*(F3F 4F1F4F6F5F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'arctanG6$*&,&*$)-%$e xpG6#%\"tG\"\"#\"\"\"F/F/!\"\"F/,&F(F/F/F/F0,$*(F.F/F*F/F1F0F/" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\312\340\352\356\345 \346\345 \360 \345\370\345\355\350\345 \342\347\377\362\374 \350\347 \362\356\343 \356, \367\362\356 \361\362\356\350\362 \342 \361\352\356\341\352\340 \365? " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 " \321 \362\356\367\352 \350 \347\360\345\355\350\377 \361\350\355\362\340\352\361\350\361\340 \342 \356\357\360\345\344\345\353\345\355\350\350 " }{TEXT 274 6 "ar ctan" }{TEXT -1 11 " (\361\354. Help)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "arctan(1,-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-% 'arctanG6##\"\"\"\"\"$!\"\"%#PiGF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "\360\345\370\345\355\350\345\354 \344\356\353\346\355\356 \341 \373\362\374" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "yt:=t->arct an((exp(t)^2-1)/(2*exp(t)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ytG f*6#%\"tG6\"6$%)operatorG%&arrowGF(-%'arctanG6#,$*&#\"\"\"\"\"#F2*&,&* $)-%$expG6#9$F3F2F2F2!\"\"F2F8F " 0 "" {MPLTEXT 1 0 30 "simplify (subs(y(t)=yt(t),de));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,$*(\"\"#\" \"\",&-%$expG6#%\"tGF'-F*6#,$F,!\"\"F'F',(F&F'-F*6#,$*&F&F'F,F'F'F'-F* 6#,$*&F&F'F,F'F0F'F0F',$*&F&F'F1#F0F&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "\314\373 \357\356\353\363\367\350\353\350 \362\356\346 \344\345\361\362\342\356, \362\340\352 \352\340\352 " }}{PARA 0 "" 0 " " {TEXT -1 2 " " }{OLE 1 5122 1 "[xm]Br=WfoRrB:::wk;nyyI;G:;:j::>:B>N :F:nyyyyy]::yyyyyy:::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::fyyyyya:nYf::G:I:K:wAyA:::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::JcvGYMt>^:fBWMtNHm=; :::::::n:;`:Z@[::JJXjxXoBiucAj;J:]Z:B:F:YLpfF>::::::: ::J?NZ;vyyyyyY:vYxY:B:::::::c:;:ElrfH=MtFGYMq>>Wlj:gmlJ::::::>^:N:yyyx I:;Z::::::j:>:mU:B:F:AlqfG[maNFO=;::::::::_J;Zy=J:B::::::f:;jn>:;:wyyN :j>J?>:Q:S:UJ:n;F<>\\:B:wA_J:V<^:SJbgZ;b;KBKaTMcdGZK^ZG_dZf br_hlGF_J>@lQPnAMnQ@NbLYBxj]xoZ:yayQ:>:fpIjZEZ:nr?j:F;HjkE:Ij]?:;j<@[C:>Z::::::::kJ;@j:>:?B:;B:yayA:;B::::::v:;J>T:<:=ja:;B:;::::::::: N[:B:yay=J:B::::::nyyyYB:::::::::::::yay=J:B:::::::::::::::::::jysy:>: <::::::::=J:f:FZ :JGvyyuy;B:[Z:>ryyYMwyyyy;b=F_<:oi:>Z::DJ<B:oqZ:f:F[:cJd@j Z:VyZ:b:;B>cTTUUSZZ:WMnAusYqrAusYQJLB:DZJ::fG:]A;;;B\\_K;b>Zn[:: jIhJm:UK<^:>x;VZ:F;;JSd::;b:<;VH::F X>>v=:Uk;^:>XCB:UZ:N`DZ:^:^hn_hnwg=vq<^Z=^q;:cb:;JaHJHjw?JB:>LJ:D::::F X>>:jP^:C:[q;f;N@B:C:EUSEUSgi:iw:ie:HZ:JD^Dqi;s:qQKZ:JB?:@Z<>:aTXDpql@ osjqJRhJ?LM@hWC:]A;;:f_;^:C:[q;f;N`DZ:^:V_efaenxH_gOfikBVBZZZ:FX>[dvJtQ;;BwE<:[j[FBxr\\N?vK;JB>bnUJ yEL<[;;ve?kZJ:>Z;NZJ?@J:bc:CjOZ=hF^=h:N:b:;rZc]:N[ <:rZE=:B;D;>KD:c=;R:=B:O:u;Hrl::?B:LAd:h:OB:B:oQ:B::C:Uk;v:^Y;B:<:^:f?EJHB:qQBv:>:sg:Bm=b:?bBaTXaEWEUUv=>Z:N;=K? AZ:B:yayaa_Q\\:^:f?GJZ:>::::WTJWTLB::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::5:" }{TEXT -1 1 " " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 " \315\340\365\356\344\350\354 \342 Mathematica \344\360\363\343\356\345 \362\356\367\355\356\345 \360\345\370\345\355\350\345, \352\356\362 \356\360\356\345 \344\356\353\346\355\356 \363\344\356\342\353\345\362 \342\356\360\377\362\374 de. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify( 2*arctan(tanh(t/2)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#\"\"\"-%'arctanG6#-%%tanhG6#,$*&F%!\"\"%\"tGF& F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "simplify(subs(y(t )=2*arctan(tanh(t/2)),de));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%dif fG6$,$*&\"\"#\"\"\"-%'arctanG6#-%%tanhG6#,$*&F)!\"\"%\"tGF*F*F*F*F4-%$ cosG6#F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "\316\344\355\340\352 \356 \350 \347\344\345\361\374 Maple \355\345 \354\356\346\345\362 \+ \363\357\360\356\361\362\350\362\374 \345\343\356 \344\356 \362\356 \346\344\345\361\362\342\340!? " }}{PARA 0 "" 0 "" {TEXT -1 52 "\316 \361\362\340\345\362\361\377 \342\356\357\360\356\361 - \352\340\352 \+ \350\362\345\360\357\360\345\362\350\360\356\342\340\362\374 \360\345 \370\345\355\350\345 resh? " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify(arctan(tanh(z))); k:=1.1:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'arctanG6#-%%tanhG6#%\"zG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "\304\340\344\350\354 \343\360\340\364\350\367\345\361\352\363\376 \+ \350\353\353\376\361\362\360\340\366\350\376 \357\360\345\344\357\356 \353\340\343\340\345\354\373\365 \360\345\370\345\355\350\351, \357 \345\360\342\356\345 \350\347 \352\356\362\356\360\373\365 " }}{PARA 0 "" 0 "" {TEXT -1 57 "\357\356\353\363\367\345\355\356 \342 Mathemati ca \350 \344\345\351\361\362\342\350\362\345\353\374\355\356 \377\342 \353\377\345\362\361\377 \360\345\370\345\355\350\345\354:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot([2*arctan(tanh(t/2)),k*yt(t)], t=0..2,color=[red,black]);" }}{PARA 13 "" 1 "" {GLPLOT2D 560 291 291 {PLOTDATA 2 "6&-%'CURVESG6$7dw7$$\"\"!F)F(7$$\"08D]+@:0\"!#;$\"0%Q%yi, :0\"F-7$$\"0BX!4QWm>F-$\"0OGs3F-7$$\"0xa4>q`*HF-$\"0=+;PA\\*HF-7$$ 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