{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 74 "Example of solving an ODE using a power series and Maple's POWS
ERIES tools" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 16 "with(powseries):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "deq:=diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$deqG/,(-%%diffG6$-%\"yG6#%\"xG-%\"$
G6$F-\"\"#\"\"\"*&F-F2-F(6$F*F-F2F2*&F1F2F*F2F2\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "inits:=y(0)=a[0],D(y)(0)=a[1];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&initsG6$/-%\"yG6#\"\"!&%\"aGF)/--%\"DG6#F
(F)&F,6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "IVP:=\{de
q,inits\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$IVPG<%/--%\"DG6#%\"yG
6#\"\"!&%\"aG6#\"\"\"/-F+F,&F/F,/,(-%%diffG6$-F+6#%\"xG-%\"$G6$F<\"\"#
F1*&F<F1-F86$F:F<F1F1*&F@F1F:F1F1F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "f:=powsolve(IVP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"fGf*6#%(powparmG6$%#nnG%#t1G6#%aoCopyright~(c)~1990~by~the~Univers
ity~of~Waterloo.~All~rights~reserved.GE\\s$\"\"!&%\"aG6#F.\"\"\"&F06#F
2%#_kG,$*&-%\"aG6#,&F5F2\"\"#!\"\"F2,&F5F2F2F=F=F=C$@%-%%typeG6$9$%(in
tegerGC$>8$-9!6#F5@%30-%#opG6$\"\"%-FP6#FJ%%NULLG-%$hasG6$7#-%(indices
G6#FOF5C%>8%-%%subsG6$/F5FDFH>-FJ6#9\"-%%evalG6#FinOFboO.F_oC$>F_oFgoO
Fgo7-%3powseries/solveeqnG,&*&,&*$)%\"kGF<F2F2FbpF=F2&%#akGF1F2F2*&Fbp
F2&Fdp6#!\"#F2F2F<F<F.%\"xG7$F/F3F<FdpFbpF96\"F[qF[q" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 19 "F:=tpsform(f,x,12);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%\"FG+=%\"xG&%\"aG6#\"\"!F*&F(6#\"\"\"F-,$F'!\"\"\"\"#
,$*&#F-F0F-F+F-F/\"\"$,$*&#F-F4F-F'F-F-\"\"%,$*&#F-\"\")F-F+F-F-\"\"&,
$*&#F-\"#:F-F'F-F/\"\"',$*&#F-\"#[F-F+F-F/\"\"(,$*&#F-\"$0\"F-F'F-F-F<
,$*&#F-\"$%QF-F+F-F-\"\"*,$*&#F-\"$X*F-F'F-F/\"#5,$*&#F-\"%SQF-F+F-F/
\"#6-%\"OGF,\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "#We can
 look at the recursion relationships:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "f(_k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%\"aG6#
,&%#_kG\"\"\"\"\"#!\"\"F*,&F)F*F*F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "#Or, more succinctly:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "recursion_relation:=a(n)=subs(_k=n,f(_k));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%3recursion_relationG/-%\"aG6#%\"nG,$*&-%\"
aG6#,&F)\"\"\"\"\"#!\"\"F0,&F)F0F0F2F2F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 74 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }