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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 55 "  second-order ODE:  y'' + ay' +  by = cubic polynomial" }}
{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 17 "define polynomial" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "P := a3*t^3 + a2*t^2 + a1*t \+
+ a0;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 20 "define solution form" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Y := c3*t^3 + c2*t^2 + c1*t + c0;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 19 "substitute into ODE" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "ode := collect(diff(Y,t,t) + a*(diff(Y,t)) + b*Y,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 45 "co := solve(identity(ode=P,t),\{c3,c2,c1,c0\});" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "part_sol := subs(co,Y);" }}}
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la" }}}}{MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }
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