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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "eq:=diff(y(x),x,x)-4
*x*diff(y(x),x)+(4*x^2-2)*y(x)-4*x^4+3;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#eqG,,-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"#\"\"\"*(\"\"%F1F,F
1-F'6$F)F,F1!\"\"*&,&*&F3F1)F,F0F1F1F0F6F1F)F1F1*&F3F1)F,F3F1F6\"\"$F1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "y1:=exp(x^2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%$expG6#*$)%\"xG\"\"#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y2:=x*exp(x^2);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#y2G*&%\"xG\"\"\"-%$expG6#*$)F&\"\"#F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 
1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee
n redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "W:=wronskian([y1,y2],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
WG-%'matrixG6#7$7$-%$expG6#*$)%\"xG\"\"#\"\"\"*&F/F1F*F17$,$*(F0F1F/F1
F*F1F1,&F*F1*(F0F1F.F1F*F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 41 "W:=simplify(W[1,1]*W[2,2]-W[1,2]*W[2,1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"WG-%$expG6#,$*&\"\"#\"\"\")%\"xGF*F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "r:=4*x^4-3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"rG,&*&\"\"%\"\"\")%\"xGF'F(F(\"\"$!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "up:=simplify(-r*y2/W);  u:=simplify
(int(up,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#upG,$*(,&*&\"\"%\"
\"\")%\"xGF)F*F*\"\"$!\"\"F*F,F*-%$expG6#,$*$)F,\"\"#F*F.F*F." }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG,$*&#\"\"\"\"\"#F(*&-%$expG6#,$*
$)%\"xGF)F(!\"\"F(,(*&\"\"%F()F1F5F(F(*&\"\")F(F0F(F(\"\"&F(F(F(F(" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "vp:=simplify(r*y1/W);   v:=
simplify(int(vp,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vpG*&,&*&\"
\"%\"\"\")%\"xGF(F)F)\"\"$!\"\"F)-%$expG6#,$*$)F+\"\"#F)F-F)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"vG,$*(%\"xG\"\"\"-%$expG6#,$*$)F'\"\"#F(
!\"\"F(,&*&F/F(F.F(F(\"\"$F(F(F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "yp:=simplify(u*y1+v*y2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#ypG,&*$)%\"xG\"\"#\"\"\"F*#\"\"&F)F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eval(eq,y(x)=yp);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,*\"\"&\"\"\"*&\"\")F%)%\"xG\"\"#F%!\"\"*&,&*&\"\"%F
%F(F%F%F*F+F%,&*$F(F%F%#F$F*F%F%F%*&F/F%)F)F/F%F+" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "eq:=diff(y(x),x,x)+2*diff(y(x),x)-3
*y(x)-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG,*-%%diffG6$-%\"yG6#
%\"xG-%\"$G6$F,\"\"#\"\"\"*&F0F1-F'6$F)F,F1F1*&\"\"$F1F)F1!\"\"F,F7" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ytr:=A*x+B;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$ytrG,&*&%\"AG\"\"\"%\"xGF(F(%\"BGF(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "res:=eval(eq,y(x)=ytr);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,**&\"\"#\"\"\"%\"AGF(F(*(\"\"$
F(F)F(%\"xGF(!\"\"*&F+F(%\"BGF(F-F,F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "seq(coeff(res,x,k),k=0..1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$,&*&\"\"#\"\"\"%\"AGF&F&*&\"\"$F&%\"BGF&!\"\",&*&F)F&F'
F&F+F&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A:=-1/3;  B:=2/
3*A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG#!\"\"\"\"$" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"BG#!\"#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "ytr;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"$!\"\"
%\"xG\"\"\"F&#\"\"#\"\"*F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "eval(eq,y(x)=ytr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
40 "eq:=diff(y(x),x,x)-2*diff(y(x),x)-x^2-1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#eqG,*-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"#\"\"\"*&F
0F1-F'6$F)F,F1!\"\"*$)F,F0F1F5F1F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "ytr:=(A*x^2+B*x+C)*x;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$ytrG*&,(*&%\"AG\"\"\")%\"xG\"\"#F)F)*&%\"BGF)F+F)F)%\"CGF)F)F
+F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "res:=eval(eq,y(x)=yt
r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,2*(\"\"'\"\"\"%\"AGF(%
\"xGF(F(*&\"\"#F(%\"BGF(F(*(F,F(,&*(F,F(F)F(F*F(F(F-F(F(F*F(!\"\"*(F,F
(F)F()F*F,F(F1*(F,F(F-F(F*F(F1*&F,F(%\"CGF(F1*$F3F(F1F(F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "seq(coeff(res,x,k),k=0..2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%,(*&\"\"#\"\"\"%\"BGF&F&*&F%F&%\"CGF&!
\"\"F&F*,&*&\"\"'F&%\"AGF&F&*&\"\"%F&F'F&F*,&*&F-F&F.F&F*F&F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "A:=-1/6;  B:=6/4*A;  C:=(2*B
-1)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG#!\"\"\"\"'" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"BG#!\"\"\"\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"CG#!\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 4 "ytr;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&#\"\"\"\"\"'F'*$)
%\"xG\"\"#F'F'!\"\"*&#F'\"\"%F'F+F'F-#\"\"$F0F-F'F+F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eval(eq,y(x)=ytr);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(*&\"\"#!\"\"%\"xG\"\"\"F&*(F%F(,&*&\"\"$F&F'F(F&
#F(\"\"%F&F(F'F(F&*(F%F(F,F&F'F%F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 53 "eq:=diff(y(x),x,x)+2*diff(y(x),x)+3*y(x)-3*exp(-2*x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG,*-%%diffG6$-%\"yG6#%\"xG-%\"$G6
$F,\"\"#\"\"\"*&F0F1-F'6$F)F,F1F1*&\"\"$F1F)F1F1*&F6F1-%$expG6#,$*&F0F
1F,F1!\"\"F1F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eval(L^2+
2*L+3,L=-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ytr:=A*exp(-2*x);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$ytrG*&%\"AG\"\"\"-%$expG6#,$*&\"\"#F'%\"xGF'!\"\"
F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "res:=eval(eq,y(x)=ytr
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,&*(\"\"$\"\"\"%\"AGF(-%$
expG6#,$*&\"\"#F(%\"xGF(!\"\"F(F(*&F'F(F*F(F1" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 29 "res:=simplify(res/exp(-2*x));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$resG,&*&\"\"$\"\"\"%\"AGF(F(F'!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A:=1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "ytr;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#,$*&\"\"#\"\"\"%\"xGF)!\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eval(eq,y(x)=ytr);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "eq:=diff(y(x),x,x)+diff
(y(x),x)-2*y(x)-3*exp(-2*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG
,*-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"#\"\"\"-F'6$F)F,F1*&F0F1F)F1!\"
\"*&\"\"$F1-%$expG6#,$*&F0F1F,F1F5F1F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "eval(L^2+L-2,L=-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eval(2*L+1,L=-2)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "ytr:=A*x*exp(-2*x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$ytrG*(%\"AG\"\"\"%\"xGF'-%$expG6#,$*&\"\"#F'F(F'!\"\"F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "res:=eval(eq,y(x)=ytr);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,&*(\"\"$\"\"\"%\"AGF(-%$expG6#
,$*&\"\"#F(%\"xGF(!\"\"F(F1*&F'F(F*F(F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "res:=simplify(res/exp(-2*x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$resG,&*&\"\"$\"\"\"%\"AGF(!\"\"F'F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "A:=-1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "ytr;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\"-%$expG6#,$*&\"\"#F&F%
F&!\"\"F&F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eval(eq,y(x)
=ytr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r
estart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "eq:=diff(y(x),x,
x)+diff(y(x),x)-2*y(x)-2*exp(-x)*sin(4*x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#eqG,*-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F,\"\"#\"\"\"-F'
6$F)F,F1*&F0F1F)F1!\"\"*(F0F1-%$expG6#,$F,F5F1-%$sinG6#,$*&\"\"%F1F,F1
F1F1F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eval(L^2+L-2,L=-1
+4*I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$!#=!\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 37 "ytr:=(A*sin(4*x)+B*cos(4*x))*exp(-x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ytrG*&,&*&%\"AG\"\"\"-%$sinG6#,$*&
\"\"%F)%\"xGF)F)F)F)*&%\"BGF)-%$cosGF,F)F)F)-%$expG6#,$F0!\"\"F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "res:=eval(eq,y(x)=ytr);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,**&,&*(\"#;\"\"\"%\"AGF*-%$sin
G6#,$*&\"\"%F*%\"xGF*F*F*!\"\"*(F)F*%\"BGF*-%$cosGF.F*F3F*-%$expG6#,$F
2F3F*F**&,&*(F1F*F+F*F6F*F**(F1F*F5F*F,F*F3F*F8F*F3*(\"\"#F*,&*&F+F*F,
F*F**&F5F*F6F*F*F*F8F*F3*(FAF*F8F*F,F*F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "res:=simplify(res/exp(-x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$resG,,*(\"#=\"\"\"%\"AGF(-%$sinG6#,$*&\"\"%F(%\"xGF(
F(F(!\"\"*(F'F(%\"BGF(-%$cosGF,F(F1*(F/F(F)F(F4F(F1*(F/F(F3F(F*F(F(*&
\"\"#F(F*F(F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "\{coeff(re
s,sin(4*x)),coeff(res,cos(4*x))\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
<$,(*&\"#=\"\"\"%\"AGF'!\"\"*&\"\"%F'%\"BGF'F'\"\"#F),&*&F&F'F,F'F)*&F
+F'F(F'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "evalm(matrix(2
,2,[4,18,18,-4]) &* [0,2]/(-4*4-18^2));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7$#!\"*\"#&)#\"\"#F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "A:=-9/85;  B:=2/85;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"AG#!\"*\"#&)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG#\"\"#\"#&
)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "ytr;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&,&*&#\"\"*\"#&)\"\"\"-%$sinG6#,$*&\"\"%F)%\"xGF)F)F
)!\"\"*&#\"\"#F(F)-%$cosGF,F)F)F)-%$expG6#,$F0F1F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "eval(eq,y(x)=ytr);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,**&,&*&#\"$W\"\"#&)\"\"\"-%$sinG6#,$*&\"\"%F*%\"xGF*F*
F*F**&#\"#KF)F*-%$cosGF-F*!\"\"F*-%$expG6#,$F1F7F*F**&,&*&#\"#OF)F*F5F
*F7*&#\"\")F)F*F+F*F7F*F8F*F7*(\"\"#F*,&*&#\"\"*F)F*F+F*F7*&#FEF)F*F5F
*F*F*F8F*F7*(FEF*F8F*F+F*F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 
"eq:=diff(y(x),x,x)-2*diff(y(x),x)+7*y(x)-x^4*exp(-x)*sin(3*x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG,*-%%diffG6$-%\"yG6#%\"xG-%\"$G6
$F,\"\"#\"\"\"*&F0F1-F'6$F)F,F1!\"\"*&\"\"(F1F)F1F1*()F,\"\"%F1-%$expG
6#,$F,F5F1-%$sinG6#,$*&\"\"$F1F,F1F1F1F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "eval(L^2-2*L+7,L=-1+3*I);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#^$\"\"\"!#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
78 "ytrial:=exp(-x)*(add(A[k]*x^k,k=0..4)*sin(3*x)+add(B[k]*x^k,k=0..4
)*cos(3*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ytrialG*&-%$expG6#,
$%\"xG!\"\"\"\"\",&*&,,&%\"AG6#\"\"!F,*&&F16#F,F,F*F,F,*&&F16#\"\"#F,)
F*F:F,F,*&&F16#\"\"$F,)F*F?F,F,*&&F16#\"\"%F,)F*FDF,F,F,-%$sinG6#,$*&F
?F,F*F,F,F,F,*&,,&%\"BGF2F,*&&FNF6F,F*F,F,*&&FNF9F,F;F,F,*&&FNF>F,F@F,
F,*&&FNFCF,FEF,F,F,-%$cosGFHF,F,F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "res:=eval(eq,y(x)=ytrial):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 27 "res:=simplify(res/exp(-x));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$resG,bp*&)%\"xG\"\"%\"\"\"-%$sinG6#,$*&\"\"$F*F(F*F*
F*!\"\"*&F+F*&%\"AG6#\"\"!F*F**&-%$cosGF-F*&%\"BGF5F*F**(F)F*F+F*&F46#
F*F*F1*(\"#7F*F8F*F3F*F1*(F)F*F8F*&F;F>F*F1*(F@F*F+F*F:F*F**(\"\"#F*F+
F*&F46#FEF*F**(\"\"'F*F8F*F=F*F**(FEF*F8F*&F;FGF*F**(FIF*F+F*FBF*F1**F
@F*F+F*FKF*)F(FEF*F**(F+F*F=F*F(F*F**(F+F*FFF*FNF*F**(F+F*&F46#F0F*)F(
F0F*F**(F+F*&F46#F)F*F'F*F**(F8F*FBF*F(F*F**(F8F*FKF*FNF*F**(F8F*&F;FS
F*FTF*F**(F8F*&F;FWF*F'F*F***\"\")F*F+F*FFF*F(F*F1**F@F*F+F*FRF*FNF*F1
**\"#;F*F+F*FVF*FTF*F1**F@F*F8F*F=F*F(F*F1**F@F*F8F*FFF*FNF*F1**F@F*F8
F*FRF*FTF*F1**F@F*F8F*FVF*F'F*F1**FinF*F8F*FKF*F(F*F1**F@F*F8F*FenF*FN
F*F1**F\\oF*F8F*FgnF*FTF*F1**F@F*F+F*FBF*F(F*F***F@F*F+F*FenF*FTF*F***
F@F*F+F*FgnF*F'F*F***FIF*F+F*FRF*F(F*F***F@F*F+F*FVF*FNF*F***F@F*F8F*F
FF*F(F*F***\"#=F*F8F*FRF*FNF*F***\"#CF*F8F*FVF*FTF*F***FIF*F8F*FenF*F(
F*F***F@F*F8F*FgnF*FNF*F***F@F*F+F*FKF*F(F*F1**F[pF*F+F*FenF*FNF*F1**F
]pF*F+F*FgnF*FTF*F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "seq(
coeff(coeff(res,sin(3*x)),x,k),k=0..4);" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6',,&%\"AG6#\"\"!\"\"\"*&\"\"%F(&F%6#F(F(!\"\"*&\"#7F(&%\"BGF&F(F(
*&\"\"#F(&F%6#F3F(F(*&\"\"'F(&F1F,F(F-,,F+F(*&\"\")F(F4F(F-*&F/F(F8F(F
(*&F7F(&F%6#\"\"$F(F(*&F/F(&F1F5F(F-,,*&F/F(FBF(F(F4F(*&F/F(F>F(F-*&F/
F(&F%6#F*F(F(*&\"#=F(&F1F?F(F-,*F>F(*&\"#;F(FGF(F-*&F/F(FKF(F(*&\"#CF(
&F1FHF(F-,(F(F-FGF(*&F/F(FRF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "seq(coeff(coeff(res,cos(3*x)),x,k),k=0..4);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6',,&%\"BG6#\"\"!\"\"\"*&\"#7F(&%\"AGF&F(!\"\"*&\"\"%F(
&F%6#F(F(F-*&\"\"'F(&F,F1F(F(*&\"\"#F(&F%6#F6F(F(,,F0F(*&F*F(F4F(F-*&
\"\")F(F7F(F-*&F*F(&F,F8F(F(*&F3F(&F%6#\"\"$F(F(,,F7F(*&F*F(F>F(F-*&F*
F(F@F(F-*&\"#=F(&F,FAF(F(*&F*F(&F%6#F/F(F(,*F@F(*&F*F(FHF(F-*&\"#;F(FJ
F(F-*&\"#CF(&F,FKF(F(,&FJF(*&F*F(FRF(F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 95 "solve(\{%,%%\},\{seq(A[k],k=0..4),seq(B[k],k=0..4)\})
; # 'solve' we use only with special pemission" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#<,/&%\"BG6#\"\"!#\"+)o%H*z\"\",D1M(4k/&%\"AGF'#!+;#)*H(
zF+/&F.6#\"\"\"#!*oBs/\"\"*D10U%/&F&F3#\")C!*QbF7/&F.6#\"\"##!'KBi\"(D
'[I/&F&F>#\"'wDhFB/&F.6#\"\"$#!%7<\"&D5#/&F&FI#\"%;QFM/&F.6#\"\"%#F4\"
$X\"/&F&FT#\"#7FW" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign
(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ytrial;" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#*&-%$expG6#,$%\"xG!\"\"\"\"\",&*&,,#\"+;#)*H(z
\",D1M(4kF)*&#\"*oBs/\"\"*D10U%F*F(F*F)*&#\"'KBi\"(D'[IF**$)F(\"\"#F*F
*F)*&#\"%7<\"&D5#F**$)F(\"\"$F*F*F)*&#F*\"$X\"F**$)F(\"\"%F*F*F*F*-%$s
inG6#,$*&FBF*F(F*F*F*F**&,,#\"+)o%H*z\"F0F**&#\")C!*QbF4F*F(F*F**&#\"'
wDhF8F*F9F*F**&#\"%;QF?F*F@F*F**&#\"#7FEF*FFF*F*F*-%$cosGFKF*F*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eval(eq,y(x)=ytrial):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"!" }}}}{MARK "73 0 0" 60 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }