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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 32 "define two homogeneous solutions" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "y1 \+
:=   exp(-2*t);" }{TEXT -1 0 "" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y1G-%$expG6#,$%\"tG!\"#" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 18 "y2 := t*exp(-2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#y2G*&%\"tG\"\"\"-%$expG6#,$F&!\"#F'" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 28 "construct linear combination" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "y := a*y2 + b*y1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&*(%\"aG\"\"\"%\"tGF(-%$expG6#,$F)!\"
#F(F(*&%\"bGF(F*F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "check if \+
y(t) is a solution" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 39 "ode := diff(y,t,t) + 4*diff(y,t) + 4*y;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$odeG\"\"!" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "result doesn't depend on \+
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