{VERSION 4 0 "APPLE_PPC_MAC" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 
0 1 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "W:=proc(f,j,k);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "# procedure qui resout x\"+k^2*x=f \+
,x(0)=0, x'(0)=0 " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "l:=array(0..j)
; m:=array(1..j);S:=\{seq(i, i=1..j)\} minus \{k\}; ;" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 22 "for q from 1 to j do; " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 102 "l[q]:=coeff(f,cos(q*t)); m[q]:=coeff(f,sin(q*t));od;
 l[0]:=f-add(l[r]*cos(r*t)+m[r]*sin(r*t), r=1..j);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 108 "add(1/(k^2-r^2)*l[r]*(cos(r*t)-cos(k*t))+1/(k^2-r^
2)*m[r]*(sin(r*t)-sin(k*t)), r=S)+1/k^2*l[0]*(1-cos(k*t));" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 9 "end proc:" }}{PARA 7 "" 1 "" {TEXT -1 59 "Wa
rning, `l` is implicitly declared local to procedure `W`\n" }}{PARA 7 
"" 1 "" {TEXT -1 59 "Warning, `m` is implicitly declared local to proc
edure `W`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `S` is implicitly
 declared local to procedure `W`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "War
ning, `q` is implicitly declared local to procedure `W`\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "T:=proc(k,n);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "u:=array(0..n); x:=array(0..n);u[0]:=cos(k*t); x[0]:=
k^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "v:=sum(u[j]*y^j, j=0..n); z
:=sum(x[j]*y^j, j=0..n)+y*cos(2*t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "P:=collect(expand(v*z),trig):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "for j from 1 to n do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "F:=com
bine(coeff(P,y,j)-k^2*u[j]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "u[j
]:=W(-F,2*j*k+2,k);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "C:=\{coeff(F
,cos(k*t)), coeff(F, sin(k*t))\};" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "V:=solve(C,x[j]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "subs(V, x[
j]);x[j]:=%;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "od;[eval(z-y*cos(2*
t)),eval(v)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 0 "" {TEXT -1 0 "" }}{PARA 
7 "" 1 "" {TEXT -1 59 "Warning, `u` is implicitly declared local to pr
ocedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `x` is implicit
ly declared local to procedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "W
arning, `v` is implicitly declared local to procedure `T`\n" }}{PARA 
7 "" 1 "" {TEXT -1 59 "Warning, `z` is implicitly declared local to pr
ocedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `P` is implicit
ly declared local to procedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "W
arning, `j` is implicitly declared local to procedure `T`\n" }}{PARA 
7 "" 1 "" {TEXT -1 59 "Warning, `F` is implicitly declared local to pr
ocedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `C` is implicit
ly declared local to procedure `T`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "W
arning, `V` is implicitly declared local to procedure `T`\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "S:=proc(k,n):" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "u:=array(0..n); x:=array(0..n);u[0]:=sin(k*t);
 x[0]:=k^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "v:=sum(u[j]*y^j, j=0
..n); z:=sum(x[j]*y^j, j=0..n)+y*cos(2*t);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "P:=collect(expand(v*z),trig):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "for j from 1 to n do;" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 34 "F:=combine(coeff(P,y,j)-k^2*u[j]);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "u[j]:=W(-F,2*j*k+2,k); " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "C:=\{coeff(F,cos(k*t)), coeff(F, sin(k*t))\};" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "V:=solve(C,x[j]);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 23 "subs(V, x[j]);x[j]:=%;;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "od;[eval(z-" }{MPLTEXT 1 0 21 "y*cos(2*t)),eval(v)];
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc:" }}{PARA 7 "" 1 "" 
{TEXT -1 59 "Warning, `u` is implicitly declared local to procedure `S
`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `x` is implicitly declare
d local to procedure `S`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `v
` is implicitly declared local to procedure `S`\n" }}{PARA 7 "" 1 "" 
{TEXT -1 59 "Warning, `z` is implicitly declared local to procedure `S
`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `P` is implicitly declare
d local to procedure `S`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `j
` is implicitly declared local to procedure `S`\n" }}{PARA 7 "" 1 "" 
{TEXT -1 59 "Warning, `F` is implicitly declared local to procedure `S
`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `C` is implicitly declare
d local to procedure `S`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `V
` is implicitly declared local to procedure `S`\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "p:=plot
([S(1,3)[1],T(1,3)[1],S(2,3)[1],T(2,3)[1]],y=-3..3):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "with(plottools): rotate(p,-Pi/2);" }}}
{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"\"F$*&#F$\"\"#F$%\"xGF$!
\"\"*&#F$\"#KF$*$)F(F'F$F$F)*&#F$\"$7&F$)F(\"\"$F$F$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7$,*\"
\"\"F%*&#F%\"\"#F%%\"yGF%F%*&#F%\"#KF%*$)F)F(F%F%!\"\"*&#F%\"$7&F%*$)F
)\"\"$F%F%F/,*-%$sinG6#%\"tGF%*&,&-F86#,$F:F5#F%\"#;*&#F%FAF%F7F%F/F%F
)F%F%*&,&-F86#,$F:\"\"&#F%\"$o(*&#F%FKF%F7F%F/F%F.F%F%*&,*F=#F/\"%'4%*
&#FI\"&wX#F%F7F%F%*&#F%\"&ko$F%FFF%F%*&#F%\"&GP(F%-F86#,$F:\"\"(F%F%F%
F4F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0
" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }