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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 40 "  second-order ODE:  y'' - y' +  y = t^2" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 32 "clear workspace & load ODE stuff" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 20 "define solution form" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "Y := A*t^2 + B*t + C;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"YG,(*&%\"AG\"\"\")%\"tG\"\"#F(F(*&%\"BGF(F*F(F(%\"C
GF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "substitute into ODE" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "ode := collect(diff(Y,t,t) -
 (diff(Y,t)) + Y,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG,,*&%\"
AG\"\"\")%\"tG\"\"#F(F(*&,&%\"BGF(*&F+F(F'F(!\"\"F(F*F(F(*&F+F(F'F(F(%
\"CGF(F.F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 35 "solve for undetermined coefficients" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 41 "co := solve(identity(ode=t^2,t),\{A,B,C\});" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#coG<%/%\"BG\"\"#/%\"AG\"\"\"/%\"C
G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "part_sol := subs(
co,Y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)part_solG,&%\"tG\"\"#*$)F
&F'\"\"\"F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 5 "voila" }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 
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