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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "# Solving non-homogeneous \+
linear equations with constant coefficients\n\n# filename = 04.3.mws\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "# Example 1\ny[p]:=x->-3*sin(x)/2;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "diff(y[p](x),x$2)-2*dif
f(y[p](x),x)+y[p](x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Example 2
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "y[p]:=x->-1/5*exp(-2*x)
*cos(x)+2/5*exp(-2*x)*sin(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 47 "diff(y[p](x),x$2)+6*diff(y[p](x),x)+13*y[p](x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "dsolve(diff(Y(x),x$2)+6*diff(Y(x),x
)+13*Y(x)=0,Y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "y[h]:
=x->_C1*exp(-3*x)*sin(2*x)+_C2*exp(-3*x)*cos(2*x):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 22 "Y:=x->y[h](x)+y[p](x):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 45 "toplot:=[seq(seq(Y(x),_C1=-1..1),_C2=-1..1)]
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(toplot,x=0..2);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Example 3" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 83 "y:='y':\ngensol:=dsolve(diff(y(x),x$2)-2*diff(
y(x),x)+y(x)=2*exp(-2*x)*sin(x),y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "partsol:=dsolve(\{diff(y(x),x$2)+y(x)=cos(omega*x),y(
0)=0,D(y)(0)=0\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "
step2:=combine(partsol,trig);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "omegavals:=[seq(2/9*i,i=0..8)]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "somegraphs:=[seq(plot(subs(omega=i,rhs(step2)),x=0..1
2*Pi,\n\011\011color=BLACK),i=omegavals)]:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 80 "with(plots):\n  anarray:=display(somegraphs,inseque
nce=true):\n  display(anarray);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 68 "partsol:=dsolve(\{diff(y(x),x$2)+y(x)=cos(x),y(0)=0,D(y)(0)=0
\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "step2:=combine
(partsol,trig);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(rhs
(step2),x=0..12*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
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