{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {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 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 42 "Example: Using DSOLVE with a p ower series" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Order:=12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&O rderG\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "deq:=diff(y(x) ,x$2)+x*diff(y(x),x)+2*y(x)=sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$deqG/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"*&F-F2-F(6$F*F- F2F2*&F1F2F*F2F2-%$sinGF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "inits:=y(1)=a[0],D(y)(1)=a[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%&initsG6$/-%\"yG6#\"\"\"&%\"aG6#\"\"!/--%\"DG6#F(F)&F,F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "IVP:=\{deq,inits\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$IVPG<%/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F.\"\"# \"\"\"*&F.F3-F)6$F+F.F3F3*&F2F3F+F3F3-%$sinGF-/-F,6#F3&%\"aG6#\"\"!/-- %\"DG6#F,F<&F>F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "F:=dsol ve(IVP,y(x),'series');" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"FG/-%\"y G6#%\"xG+=,&F)\"\"\"F,!\"\"&%\"aG6#\"\"!F1&F/6#F,F,,(*&#F,\"\"#F,F2F,F -F.F-*&#F,F7F,-%$sinGF3F,F,F7,**&#F,\"\"$F,F.F,F,*&#F,\"\"'F,F:F,F-*&# F,F?F,F2F,F-*&#F,FBF,-%$cosGF3F,F,F?,**&#F,\"\"%F,F2F,F,*&FKF,F.F,F,*& #F,FBF,F:F,F-*&#F,\"#CF,FGF,F-FL,**&#F7\"#:F,F.F,F-*&#F?\"#SF,F:F,F,*& #F,FRF,FGF,F-*&#F,\"#IF,F2F,F,\"\"&,**&#F,\"#=F,F2F,F-*&#F,\"#OF,F.F,F -*&#F,\"#XF,F:F,F,*&#\"#6\"$?(F,FGF,F,FB,**&#Ffo\"$?%F,F.F,F,*&#\"#z\" %S]F,F:F,F-*&#Fin\"%35F,FGF,F,*&#F,F[pF,F2F,F,\"\"(,**&#Ffo\"%S9F,F2F, F,*&#F,FipF,F.F,F,*&#Fin\"%KSF,F:F,F-*&#\"$8\"\"&?.%F,FGF,F-\"\"),**&# \"#>\"%qcF,F.F,F-*&#\"$h(\"'!)GOF,F:F,F,*&#FaqF\\rF,FGF,F-*&#\"#8\"&S8 \"F,F2F,F-\"\"*,**&#\"#P\"&+/&F,F2F,F-*&#FarFhrF,F.F,F,*&#Far\"'S9=F,F :F,F-*&#\"%V7\"(+)GOF,FGF,F,\"#5,**&#\"$6$\"'?z**F,F.F,F,*&#\"%6\")\") +o\"*RF,F:F,F-*&#\"$\"=FgsF,F2F,F,*&#F,F[tF,FGF,F,Ffo-%\"OGF3\"#7" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "F1:=convert(rhs(F),polynom,x );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#F1G,:&%\"aG6#\"\"!\"\"\"*&&F' 6#F*F*,&%\"xGF*F*!\"\"F*F**&,(*&#F*\"\"#F*F,F*F0F&F0*&#F*F5F*-%$sinGF- F*F*F*)F.F5F*F**&,**&#F*\"\"$F*F&F*F**&#F*\"\"'F*F8F*F0*&#F*F?F*F,F*F0 *&#F*FBF*-%$cosGF-F*F*F*)F.F?F*F**&,**&#F*\"\"%F*F,F*F**&FMF*F&F*F**&# F*FBF*F8F*F0*&#F*\"#CF*FGF*F0F*)F.FNF*F**&,**&#F5\"#:F*F&F*F0*&#F?\"#S F*F8F*F**&#F*FTF*FGF*F0*&#F*\"#IF*F,F*F*F*)F.\"\"&F*F**&,**&#F*\"#=F*F ,F*F0*&#F*\"#OF*F&F*F0*&#F*\"#XF*F8F*F**&#\"#6\"$?(F*FGF*F*F*)F.FBF*F* *&,**&#F\\p\"$?%F*F&F*F**&#\"#z\"%S]F*F8F*F0*&#F^o\"%35F*FGF*F**&#F*Fc pF*F,F*F*F*)F.\"\"(F*F**&,**&#F\\p\"%S9F*F,F*F**&#F*FcqF*F&F*F**&#F^o \"%KSF*F8F*F0*&#\"$8\"\"&?.%F*FGF*F0F*)F.\"\")F*F**&,**&#\"#>\"%qcF*F& F*F0*&#\"$h(\"'!)GOF*F8F*F**&#F[rFhrF*FGF*F0*&#\"#8\"&S8\"F*F,F*F0F*)F .\"\"*F*F**&,**&#\"#P\"&+/&F*F,F*F0*&#F]sFfsF*F&F*F**&#F]s\"'S9=F*F8F* F0*&#\"%V7\"(+)GOF*FGF*F*F*)F.\"#5F*F**&,**&#\"$6$\"'?z**F*F&F*F**&#\" %6\")\")+o\"*RF*F8F*F0*&#\"$\"=FgtF*F,F*F**&#F*F[uF*FGF*F*F*)F.F\\pF*F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 0" 42 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }