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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 50 "  higher-order undetermined coefficients (#4.3.12)" }}{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 14 "define forcing" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "G := 12*sin(t);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "define solution form" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Y := A*cos(t) + B*sin(t);" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "
substitute into ODE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "ode \+
:= collect(diff(Y,t$4) + 2*diff(Y,t$3) + diff(Y,t$2) + 8*diff(Y,t) - 1
2*Y,\{sin(t),cos(t)\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 35 "solve for undetermined coefficients" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "co := solve(identity(ode=G,t
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subs(co,Y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
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