{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 35 "" 0 1 104 64 92 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 
"Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 
}{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 
2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" 3 4 
1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 
0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Tim
es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "\324\340\351\353: \"...
\312\356\354\357\322\345\365\355\\\321\353\363\370\340\362\345\353\350
\324\317\312\317\\\320\345\370\316\341\373\352\304\350\364\323\360.mws
\" (\350\347 Help) 22.10.14\343. \322\350\362\356\342 \312.\302." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 47 "de:=a*diff(y(x),x$2)+b*diff(y(x),x$1)+c*y(x)
=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#deG/,(*&%\"aG\"\"\"-%%diffG6
$-%\"yG6#%\"xG-%\"$G6$F0\"\"#F)F)*&%\"bGF)-F+6$F-F0F)F)*&%\"cGF)F-F)F)
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "a:=1:b:=1:c:=1:de;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$
F+\"\"#\"\"\"-F&6$F(F+F0F(F0\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "re:=dsolve(de);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#reG/-%\"yG6#%\"xG,&*(%$_C1G\"\"\"-%$expG6#,$*&\"\"#!\"\"F)F-F4F--%$si
nG6#,$*(F3F4\"\"$#F-F3F)F-F-F-F-*(%$_C2GF-F.F--%$cosGF7F-F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "ics := y(0)=1, D(y)(0)=0; co
nvert(D(y)(0),diff); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$icsG6$/-%
\"yG6#\"\"!\"\"\"/--%\"DG6#F(F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%%evalG6$-%%diffG6$-%\"yG6#%#t1GF,<#/F,\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "re:=dsolve(\{de,ics\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#reG/-%\"yG6#%\"xG,&*&#\"\"\"\"\"$F-*(F.#F-\"\"#-%$ex
pG6#,$*&F1!\"\"F)F-F7F--%$sinG6#,$*(F1F7F.F0F)F-F-F-F-F-*&F2F--%$cosGF
:F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "odetest(re, de);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "odetest(re, [de, ics]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7%\"\"!F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Order:
=8: series_re := dsolve(\{de,ics\}, y(x), series);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%*series_reG/-%\"yG6#%\"xG+/F)\"\"\"\"\"!#!\"\"\"\"#
F/#F+\"\"'\"\"$#F.\"$?\"\"\"&#F+\"$?(F1-%\"OG6#F+\"\")" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "odetest(series_re, [de, ics], serie
s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"!F$F$" }}}{SECT 0 {PARA 
4 "" 0 "" {TEXT -1 21 "Solving an ODE System" }}{PARA 0 "" 0 "" {TEXT 
-1 25 "Define a system of ODEs. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 54 "sys_ode := diff(Y(t),t) = X(t),  diff(X(t),t) = -X(t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(sys_odeG6$/-%%diffG6$-%\"YG6#%\"tGF
--%\"XGF,/-F(6$F.F-,$F.!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 136 "If the \+
unknowns are not specified, all differentiated indeterminate functions
 in the system are treated as the unknowns of the problem. " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve([sys_ode]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#<$/-%\"XG6#%\"tG*&%$_C2G\"\"\"-%$expG6#,$F(!\"\"F+
/-%\"YGF',&F)F0%$_C1GF+" }}}{PARA 0 "" 0 "" {TEXT -1 27 "Define initia
l conditions. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ic := X(0)
=1, Y(1)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#icG6$/-%\"XG6#\"\"!
\"\"\"/-%\"YG6#F+F*" }}}{PARA 0 "" 0 "" {TEXT -1 59 "Solve the system \+
of ODEs subject to the initial conditions " }{TEXT 35 3 "ics" }{TEXT 
-1 2 ". " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "dsolve([sys_ode,
 ic]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"XG6#%\"tG-%$expG6#,$F
(!\"\"/-%\"YGF',&F)F-*&\"\"\"F3-F*6#F3F-F3" }}}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "re:=
 dsolve(\{de, ics\}, y(x), method=laplace);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#reG/-%\"yG6#%\"xG,$*&#\"\"\"\"\"$F-*&-%$expG6#,$*&\"
\"#!\"\"F)F-F6F-,&*&F.F--%$cosG6#,$*(F5F6F.#F-F5F)F-F-F-F-*&F.F>-%$sin
GF;F-F-F-F-F-" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 256 19 
"\316\357\345\360\340\362\356\360\355\356\345 \360\345\370\345\355\350
\345" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(inttrans):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Lp:=laplace(de,x,s);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LpG/,.*&)%\"sG\"\"#\"\"\"-%(laplace
G6%-%\"yG6#%\"xGF2F)F+F+--%\"DG6#F06#\"\"!!\"\"*&F)F+-F0F7F+F9*&F)F+F,
F+F+F;F9F,F+F8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\307\340\357
\350\361\374 \355\340\367\340\353\374\355\373\365 \363\361\353\356\342
\350\351 \342 \342\345\352\362\356\360 \350 \350\365 \350\344\345\355
\362\350\364\350\352\340\366\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "icv := [ics]; lhs(icv[1]);rhs(icv[1]);rhs(icv[2]):" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$icvG7$/-%\"yG6#\"\"!\"\"\"/--%\"DG
6#F(F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"yG6#\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "
\317\356\344\361\362\340\342\353\377\345\354 \355\340\367\340\353\374
\355\373\345 \363\361\353\356\342\350\377 \342 Lp:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 61 "Lp:=subs(lhs(icv[1])=rhs(icv[1]),lhs(icv[2]
)=rhs(icv[2]),Lp);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LpG/,,*&)%\"s
G\"\"#\"\"\"-%(laplaceG6%-%\"yG6#%\"xGF2F)F+F+F+!\"\"F)F3*&F)F+F,F+F+F
,F+\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "\315\340\365\356\344
\350\354 \360\345\370\345\355\350\345 \342 \356\357\345\360\340\362
\356\360\355\356\354 \342\350\344\345:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "s_re:=solve(Lp,laplace(y(x),x,s));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%s_reG*&,&\"\"\"F'%\"sGF'F',(*$)F(\"\"#F'F'F(F'F'F'
!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "\317\360\356\342\356\344
\350\354 \356\341\360\340\362\355\356\345 \357\360\345\356\341\360\340
\347\356\342\340\355\350\345 \313\340\357\353\340\361\340" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "invlaplace(s_re, s, x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"$F&*&-%$expG6#,$*&\"\"#!\"\"%
\"xGF&F/F&,&*&F'F&-%$cosG6#,$*(F.F/F'#F&F.F0F&F&F&F&*&F'F8-%$sinGF5F&F
&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 9 "\307\340\344\340\355
\350\345. " }{TEXT -1 69 "\310\347\354\345\355\350\362\374 \352\356
\375\364\364\350\366\350\345\355\362\373 a, b, c \350 \355\340\367\340
\353\374\355\373\345 \363\361\353\356\342\350\377 \350 \357\356\342
\362\356\360\350\362\374 \360\345\370\345\355\350\345" }}{PARA 0 "" 0 
"" {TEXT -1 23 "\342 \350\355\362\345\360\340\352\362\350\342\355\356
\354 \360\345\346\350\354\345." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "15 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 1 0 2 33 1 1 }