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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 24 "ENGI 3424 Example 5.11.2
" }}{PARA 0 "" 0 "" {TEXT -1 72 "Series Solution of a Second Order Lin
ear ODE (non-constant coefficients)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "ode := diff(y(x),x,x) + x*x*y(x) = 0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$odeG/,&-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"*
&)F-F1F2F*F2F2\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Orde
r := 15;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&OrderG\"#:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "dsolve(ode, y(x), series);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG+5F'-F%6#\"\"!F+--%\"DG6
#F%F*\"\"\",$*&#F0\"#7F0F)F0!\"\"\"\"%,$*&#F0\"#?F0F,F0F5\"\"&,$*&#F0
\"$s'F0F)F0F0\"\"),$*&#F0\"%S9F0F,F0F0\"\"*,$*&#F0\"&/())F0F)F0F5F4,$*
&#F0\"'SYAF0F,F0F5\"#8-%\"OG6#F0\"#:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 98 "In order to see the parts of the general solution more clearly,
 apply a set of initial conditions." }}{PARA 0 "" 0 "" {TEXT -1 38 "Th
e part of the solution multiplying  " }{TEXT 257 2 "y'" }{TEXT -1 7 "(
0) is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ics := y(0)=0, D(
y)(0)=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$icsG6$/-%\"yG6#\"\"!F*/
--%\"DG6#F(F)\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsol
ve(\{ode, ics\}, y(x), series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%
\"yG6#%\"xG+-F'\"\"\"F)#!\"\"\"#?\"\"&#F)\"%S9\"\"*#F+\"'SYA\"#8-%\"OG
6#F)\"#:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "The part of the solut
ion multiplying  " }{TEXT 258 1 "y" }{TEXT -1 7 "(0) is:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ics := y(0)=1, D(y)(0)=0;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$icsG6$/-%\"yG6#\"\"!\"\"\"/--%\"DG6#F(F)F
*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsolve(\{ode, ics\}, y
(x), series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG+-F'\"
\"\"\"\"!#!\"\"\"#7\"\"%#F)\"$s'\"\")#F,\"&/())F--%\"OG6#F)\"#:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "The exact solution involves Bessel
 functions (beyond the scope of this course):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "dsolve(ode, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%\"yG6#%\"xG,&*(%$_C1G\"\"\"F'#F+\"\"#-%(BesselJG6$#F+\"\"%,$*
&F-!\"\"F'F-F+F+F+*(%$_C2GF+F'F,-%(BesselYGF0F+F+" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 72 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }