{VERSION 6 0 "IBM INTEL NT" "6.0" }
{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 "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P
lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 
1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart: with(DEtool
s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7iq%)DEnormalG%'DEplotG%)DEplot
3dG%/DEplot_polygonG%(DFactorG%,DFactorLCLMG%,DFactorsolsG%+Dchangevar
G%%GCRDG%%LCLMG%,MeijerGsolsG%0PDEchangecoordsG%-RiemannPsolsG%(Xchang
eG%,XcommutatorG%'XgaugeG%(abelsolG%(adjointG%+autonomousG%-bernoullis
olG%)buildsolG%)buildsymG%'canoniG%)caseplotG%*casesplitG%*checkrankG%
)chinisolG%,clairautsolG%/constcoeffsolsG%+convertAlgG%+convertsysG%-d
alembertsolG%(dcoeffsG%*de2diffopG%+dfieldplotG%*diffop2deG%/dperiodic
_solsG%*dpolyformG%&dsubsG%*eigenringG%6endomorphism_charpolyG%'equinv
G%&eta_kG%*eulersolsG%)exactsolG%(expsolsG%/exterior_powerG%'firintG%(
firtestG%+formal_solG%(gen_expG%,generate_icG%+genhomosolG%'gensysG%-h
amilton_eqsG%.hypergeomsolsG%)hyperodeG%+indicialeqG%'infgenG%,initial
dataG%/integrate_solsG%*intfactorG%+invariantsG%,kovacicsolsG%-leftdiv
isionG%'liesolG%)line_intG%*linearsolG%)matrixDEG%/matrix_riccatiG%.ma
xdimsystemsG%-moser_reduceG%)muchangeG%%multG%'mutestG%/newton_polygon
G%)normalG2G%+odeadvisorG%'odepdeG%.parametricsolG%.phaseportraitG%)po
incareG%)polysolsG%1power_equivalentG%(ratsolsG%'redodeG%,reduceOrderG
%-reduce_orderG%.regular_partsG%*regularspG%.remove_RootOfG%/riccati_s
ystemG%+riccatisolG%(rifreadG%(rifsimpG%.rightdivisionG%(rtaylorG%-sep
arablesolG%,solve_groupG%-super_reduceG%'symgenG%0symmetric_powerG%2sy
mmetric_productG%(symtestG%)transinvG%*translateG%,untranslateG%)varpa
ramG%%zoomG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "dsolve([dif
f(y1(t),t) - 3*y1(t) - 4*y2(t) = exp(t), diff(y2(t),t) - y1(t) - 3*y2(
t) = exp(-t)],[y1(t),y2(t)]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-%
#y1G6#%\"tG,,*(\"\"#\"\"\"-%$expGF'F,%$_C2GF,!\"\"*(F+F,-F.6#,$*&\"\"&
F,F(F,F,F,%$_C1GF,F,*&#F,\"\")F,F-F,F0*&#F,F+F,*&F(F,F-F,F,F,*&#F,\"\"
$F,-F.6#,$F(F0F,F,/-%#y2GF',,*&F-F,F/F,F,*&F2F,F7F,F,*&#F,\"\"%F,F=F,F
0*&#F,\"#;F,F-F,F0*&#F,F@F,FAF,F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "?dsolve" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 
"dsolve([diff(y1(t),t) - 3*y1(t) - 4*y2(t) = exp(t), diff(y2(t),t) - y
1(t) - 3*y2(t) = exp(-t),y1(0)=1,y2(0)=1],[y1(t),y2(t)]);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#<$/-%#y1G6#%\"tG,**&#\"\"*\"\")\"\"\"-%$expGF'F
.!\"\"*&#\"#V\"#CF.-F06#,$*&\"\"&F.F(F.F.F.F.*&#F.\"\"#F.*&F(F.F/F.F.F
.*&#F.\"\"$F.-F06#,$F(F1F.F./-%#y2GF',**&#\"\"(\"#;F.F/F.F.*&#F4\"#[F.
F6F.F.*&#F.\"\"%F.F>F.F1*&#F.FAF.FBF.F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 "" 1 "" {TEXT -1 45 "Warning
, the name adjoint has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 
80 "Warning, the protected names norm and trace have been redefined an
d unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG
%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcol
G%'addrowG%$adjG%(adjointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%
'bezoutG%,blockmatrixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%
)colspaceG%(colspanG%*companionG%'concatG%%condG%)copyintoG%*crossprod
G%%curlG%)definiteG%(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotpro
dG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG
%&equalG%,exponentialG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG
%*frobeniusG%*gausselimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)had
amardG%(hermiteG%(hessianG%(hilbertG%+htransposeG%)ihermiteG%*indexfun
cG%*innerprodG%)intbasisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jac
obianG%'jordanG%'kernelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'
matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normali
zeG%*nullspaceG%'orthogG%*permanentG%&pivotG%*potentialG%+randmatrixG%
+randvectorG%%rankG%(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rre
fG%*scalarmulG%-singularvalsG%&smithG%,stackmatrixG%*submatrixG%*subve
ctorG%)sumbasisG%(swapcolG%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*t
ransposeG%,vandermondeG%*vecpotentG%(vectdimG%'vectorG%*wronskianG" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "?linsolve" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 70 "linsolve([[-2,1,-4,0],[0,-2,0,-4],[-1,0,-
2,1],[0,-1,0,-2]],[1,0,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'ve
ctorG6#7&,&*&\"\"#\"\"\"&%#_tG6#F*F*!\"\"#F*\"\"%F.#F*F)F+#F.F0Q(pprin
t06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%#y1G6#%\"tG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 127 "y1 := t -> -9/8*exp(t)+43/24*exp(5*t)+1/2*t*exp(t)+1/3*exp(-t
);\ny2 := t -> 7/16*exp(t)+43/48*exp(5*t)-1/4*t*exp(t)-1/3*exp(-t);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1Gf*6#%\"tG6\"6$%)operatorG%&arro
wGF(,**&#\"\"*\"\")\"\"\"-%$expG6#9$F1!\"\"*&#\"#V\"#CF1-F36#,$*&\"\"&
F1F5F1F1F1F1*&#F1\"\"#F1*&F5F1F2F1F1F1*&#F1\"\"$F1-F36#,$F5F6F1F1F(F(F
(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2Gf*6#%\"tG6\"6$%)operatorG%&
arrowGF(,**&#\"\"(\"#;\"\"\"-%$expG6#9$F1F1*&#\"#V\"#[F1-F36#,$*&\"\"&
F1F5F1F1F1F1*&#F1\"\"%F1*&F5F1F2F1F1!\"\"*&#F1\"\"$F1-F36#,$F5FCF1FCF(
F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "y1(0); y2(0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(y1(t),
t=-3..0.3);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6%-
%'CURVESG6$7fn7$$!\"$\"\"!$\"35P_+o%)[kl!#<7$$!3@++D\"Rp!GHF-$\"3)[\\2
(e+*>4'F-7$$!37+v=`H[lGF-$\"3Lk&pf`Loq&F-7$$!3#***\\(y&z4&z#F-$\"3#flT
sD&f+`F-7$$!3;+]70kCCFF-$\"3'ov%Hj\")\\=\\F-7$$!3)**\\PufJPl#F-$\"3c%)
>')3D2jXF-7$$!3C+v=W`N)e#F-$\"3]oM&fLuTD%F-7$$!3*)*\\(o??m?DF-$\"3O**R
fm$>Q&RF-7$$!3A+vo)[`1X#F-$\"3GR&=kEIEm$F-7$$!37+v$\\Zp3Q#F-$\"3g'>PZr
q1R$F-7$$!3<++DR!)34BF-$\"37&el;'4iGJF-7$$!3=+]i6H'eC#F-$\"3E6J++Jj6HF
-7$$!3'****\\FR'ou@F-$\"3k&)\\u4mv\"o#F-7$$!3D++D;w@.@F-$\"3]JY')HV>lC
F-7$$!3?++D2UMM?F-$\"3[r3/tK-pAF-7$$!33+vo`0!=(>F-$\"3)=FYN\"ox+@F-7$$
!3-++D+,V(*=F-$\"3]0>R4l37>F-7$$!37+++r&GW$=F-$\"3U0>$)z)>7w\"F-7$$!3;
+v=:G9h<F-$\"3%fORQ%*3`f\"F-7$$!3M++].DF'p\"F-$\"39KEX?iUc9F-7$$!3++v=
!\\*4D;F-$\"3=X]`6n,78F-7$$!37+Dc]fKd:F-$\"3/f_aWAo\"=\"F-7$$!3/+](=P6
m[\"F-$\"3!3Dllr$f_5F-7$$!3=+v$RJt;U\"F-$\"3oTOAp45)R*!#=7$$!3I+]iX)G;
N\"F-$\"3-n@%[2;!R#)F[s7$$!3M+voGB()y7F-$\"3Q]&)Ga#**Q4(F[s7$$!3O+D\"o
cPb@\"F-$\"3G$RDzI5H9'F[s7$$!3C+]())GMr9\"F-$\"3!*oA`'e48;&F[s7$$!3S++
]4qYw5F-$\"3UTW:2%)3&>%F[s7$$!3G+]PjGL25F-$\"3;wf'G?ZiH$F[s7$$!3#G+v=A
?WS*F[s$\"3C[%H'4z,rCF[s7$$!3[-+Dw9rh')F[s$\"3I-RQ))e,4;F[s7$$!3'\\++]
jaV*zF[s$\"3?!=DY4')\\)))!#>7$$!3k,+]i(3=G(F[s$\"3#z'pg)Gm;&=Fiu7$$!3&
f+voHOhj'F[s$!3:W(z7>&>2QFiu7$$!3b-+]ZdCIfF[s$!3q[<;o=X3!*Fiu7$$!3-/](
=vdgE&F[s$!3o-@+>Y)zE\"F[s7$$!3Y/]P>**yrXF[s$!3')\\%QB)e$>[\"F[s7$$!3_
/+]7i,$*QF[s$!3!*zq?*e-KY\"F[s7$$!3?/](o/.C=$F[s$!3q3Z[aRT46F[s7$$!3E*
*****4\")*z\\#F[s$!33J_oCd*f=$Fiu7$$!3[,+D6_4)z\"F[s$\"3!enyEw2;8\"F[s
7$$!3()**\\(='y)R5\"F[s$\"3yCQ'Q2C/Z$F[s7$$!3))>++]HvhYFiu$\"31i&GhM^Q
s'F[s7$$!3,B+Dcqs15Fiu$\"34I>BAf/<#*F[s7$$\"3'Q(**\\P))H[EFiu$\"3iM()G
r7OG7F-7$$\"3Eg*\\(ovR<fFiu$\"3q=;v!p?0c\"F-7$$\"3mY*****H'\\'=*Fiu$\"
35([>V7,u&>F-7$$\"3%o\\i!RP?n7F[s$\"3!>wvB6%ykCF-7$$\"3,**\\7[yv:;F[s$
\"3OXylp@CvIF-7$$\"3+)\\ilAjDy\"F[s$\"3FWyVI>W4MF-7$$\"3)p****\\go$\\>
F[s$\"33cw)pc7Tx$F-7$$\"3'f\\PM)R<;@F[s$\"35x+`T+!><%F-7$$\"3'\\*\\(=O
zHG#F[s$\"3E9<8d/o0YF-7$$\"3KYiS@XBiCF[s$\"3NvnE**o`:^F-7$$\"3p(\\P4o*
[TEF[s$\"3+8&z*)*[![n&F-7$$\"3^[(o/%[u?GF[s$\"3ixC!G47\")G'F-7$$\"3))*
*************HF[s$\"3!oL'>()*>0'pF--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F^
^l-%+AXESLABELSG6$Q\"t6\"Q!Fc^l-%%VIEWG6$;F($\"\"$F]^l%(DEFAULTG" 1 2 
0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(y2(t),t=-3..0.3);" }}
{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6%-%'CURVESG6$7U7$
$!\"$\"\"!$!3.b:ncl0Om!#<7$$!3@++D\"Rp!GHF-$!3]c;S!QLz;'F-7$$!37+v=`H[
lGF-$!3Ghj7]-z'y&F-7$$!3#***\\(y&z4&z#F-$!3]iA\\fmI&Q&F-7$$!3;+]70kCCF
F-$!3SjmhTlE3]F-7$$!3)**\\PufJPl#F-$!3'RK!p9u:eYF-7$$!3C+v=W`N)e#F-$!3
o?s-0OXaVF-7$$!3*)*\\(o??m?DF-$!3)*Q1=>!f(fSF-7$$!3A+vo)[`1X#F-$!3Ear2
9*RZx$F-7$$!37+v$\\Zp3Q#F-$!3%Rg=?gl#4NF-7$$!3<++DR!)34BF-$!31jAXTBDaK
F-7$$!3=+]i6H'eC#F-$!33wI(f;$yVIF-7$$!3'****\\FR'ou@F-$!3&4#>Br1i@GF-7
$$!3D++D;w@.@F-$!3j-g=N6A8EF-7$$!3?++D2UMM?F-$!3jc:H_\"G`U#F-7$$!33+vo
`0!=(>F-$!3Q\"egt/i\\E#F-7$$!3-++D+,V(*=F-$!3SG(=UL2h3#F-7$$!37+++r&GW
$=F-$!3$=n*)QSzR%>F-7$$!3;+v=:G9h<F-$!3!*Q&*>\"G9()y\"F-7$$!3M++].DF'p
\"F-$!3uWT'>j#pf;F-7$$!3++v=!\\*4D;F-$!3JL'>E5xl_\"F-7$$!37+Dc]fKd:F-$
!3b@J&\\H`uS\"F-7$$!3/+](=P6m[\"F-$!3uR8=J(=0H\"F-7$$!3=+v$RJt;U\"F-$!
3')H'G:hx#*=\"F-7$$!3I+]iX)G;N\"F-$!3!\\(G^'euh3\"F-7$$!3M+voGB()y7F-$
!37A#Q*QTf_)*!#=7$$!3O+D\"ocPb@\"F-$!3`=8aK\"H7-*Fes7$$!3C+]())GMr9\"F
-$!3qGAwe6Lo\")Fes7$$!3S++]4qYw5F-$!3s;+dutmJtFes7$$!3G+]PjGL25F-$!3-!
*Q[>30_lFes7$$!3#G+v=A?WS*Fes$!3uao6LF]HeFes7$$!3[-+Dw9rh')Fes$!3;9&z'
*eru0&Fes7$$!3'\\++]jaV*zFes$!3K\\atnjG%Q%Fes7$$!3k,+]i(3=G(Fes$!3webg
t!>$yOFes7$$!3&f+voHOhj'Fes$!3xjtC\")3rSIFes7$$!3b-+]ZdCIfFes$!3GRh\\S
1ZKBFes7$$!3-/](=vdgE&Fes$!31-Ru&[C(Q;Fes7$$!3Y/]P>**yrXFes$!3,dHFK1J7
')!#>7$$!3_/+]7i,$*QFes$!3QzKDfzLB<!#?7$$!3?/](o/.C=$Fes$\"3y)3=lGCN+
\"Fes7$$!3E******4\")*z\\#Fes$\"3Y%[/0\\TV=#Fes7$$!3[,+D6_4)z\"Fes$\"3
'*e(*3'>Tio$Fes7$$!3()**\\(='y)R5\"Fes$\"3'4*494Hm+cFes7$$!3))>++]HvhY
Fbw$\"3a@B=fWJ!*yFes7$$\"3'Q(**\\P))H[EFbw$\"3Gp\")*fD)[S6F-7$$\"3mY**
***H'\\'=*Fbw$\"3GciWC7Xo:F-7$$\"3,**\\7[yv:;Fes$\"3i+2#ygEE>#F-7$$\"3
)p****\\go$\\>Fes$\"3embac-SsDF-7$$\"3'\\*\\(=OzHG#Fes$\"3,dP6CF$z,$F-
7$$\"3p(\\P4o*[TEFes$\"3S=SmK:z$e$F-7$$\"3))**************HFes$\"3y5pp
p3BdUF--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F\\\\l-%+AXESLABELSG6$Q\"t6\"Q
!Fa\\l-%%VIEWG6$;F($\"\"$F[\\l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 28 "plot(diff(y2(t),t),t=-1..0);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 496 496 496 {PLOTDATA 2 "6%-%'CURVESG6$7U7$$!\"\"\"\"!$\"3/e
A$fe@s4\"!#<7$$!3!RLL$e%G?y*!#=$\"3IY(3\\-eE3\"F-7$$!3OmmT&esBf*F1$\"3
EVamENkq5F-7$$!3yKL$3s%3z$*F1$\"3%3o=\"4H*y0\"F-7$$!33LL$e/$Qk\"*F1$\"
3mA\\m&R3f/\"F-7$$!3!pm;/\"=q]*)F1$\"3$)R780>([.\"F-7$$!3'GL$3_>f_()F1
$\"39A/2dqZD5F-7$$!3))***\\(o1YZ&)F1$\"3kP^\\@sk;5F-7$$!30ML3-OJN$)F1$
\"3#*>Zl)QN&35F-7$$!3p***\\P*o%Q7)F1$\"3O9(eKS]:+\"F-7$$!3ammm\"RFj!zF
1$\"3]$[^[7Wf&**F17$$!3JLL$e4OZr(F1$\"3eYf``tb9**F17$$!3=+++v'\\!*\\(F
1$\"3M_[%=^E8))*F17$$!33+++DwZ#G(F1$\"3AVy1+>Lj)*F17$$!3[*****\\KqP2(F
1$\"3edP-X?!=')*F17$$!3OLL3-TC%)oF1$\"3U<x!z@%)\\()*F17$$!3Onmm\"4z)em
F1$\"3d)Qyy!HH5**F17$$!3+nmmm`'zY'F1$\"3EWpk\\kMe**F17$$!3!3+](=t)eC'F
1$\"3(>&om*G:P+\"F-7$$!3qnmm;1J\\gF1$\"3vX0TL\\$H,\"F-7$$!3y***\\(=[jL
eF1$\"3(R(>/2.rD5F-7$$!3\\++Dc/EGcF1$\"3=i%fS;62/\"F-7$$!35nm;aQ(RT&F1
$\"3K@Z@6\"3'f5F-7$$!3smmTg=><_F1$\"3_X=b1!o,3\"F-7$$!3VLL$e*e$\\+&F1$
\"3R2(>hILh5\"F-7$$!3;ML3-;Y%y%F1$\"3.V7L#='pP6F-7$$!3]++D\"3QDf%F1$\"
3g^*GW[t$p6F-7$$!3'QLL3Ub_Q%F1$\"3T$es]aI%37F-7$$!3O+++]@6rTF1$\"332t$
G;1YD\"F-7$$!3/,+]PZhhRF1$\"3d*Q\"*pA=hI\"F-7$$!3y++v=_\"*ePF1$\"3O!op
d%zbi8F-7$$!3*3++D'>&Q`$F1$\"3d3QngRlL9F-7$$!3Pnmm;EiJLF1$\"3MM5[Jp\"f
]\"F-7$$!3?+++D'*p:JF1$\"3[#)esfbz#f\"F-7$$!3zLL3-8/?HF1$\"3=s(Gk=16o
\"F-7$$!3<+++v]81FF1$\"3Sr\"e=,1#*y\"F-7$$!3snmT&)f'[]#F1$\"3[rk\")G75
.>F-7$$!3g++v$z\"[%H#F1$\"3\"f(*o\">y9O?F-7$$!33nmm\"z#z)3#F1$\"3q3CX@
Q`\"=#F-7$$!3Y++voaXt=F1$\"3Y&HZqMQ<N#F-7$$!33LLLL+1m;F1$\"3)Q>Vyev\\`
#F-7$$!3iLL$eCoRX\"F1$\"3S[vSLw7WFF-7$$!3$om;aoKOC\"F1$\"3IGKH@XnvHF-7
$$!3E+++]hN]5F1$\"3xZz\"f&))*=@$F-7$$!3anmm\"H%R)G)!#>$\"3w=R5i#)G8NF-
7$$!30PLLLB72jFcy$\"3sqR)\\tfN\"QF-7$$!3i(***\\(=tY>%Fcy$\"3;O1!Qhv\"p
TF-7$$!3s(******\\JP=$Fcy$\"3k2#)GN5X`VF-7$$!3#y***\\7)*ys@Fcy$\"35*3$
R%o$\\ZXF-7$$!3#*)**\\i!\\R'3\"Fcy$\"3i<F=*o%[nZF-7$$F*F*$\"\"&F*-%'CO
LOURG6&%$RGBG$\"#5F)F`[lF`[l-%+AXESLABELSG6$Q\"t6\"Q!F]\\l-%%VIEWG6$;F
(F`[l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 
0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot([y1(t
),y2(t),t=-1..0.1]);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 
{PLOTDATA 2 "6%-%'CURVESG6$7Y7$$\"3!3;h&f+i.K!#=$!3/5I%\\\\29Z'F*7$$\"
3M$pm$RJV/HF*$!3t_g7$ei-@'F*7$$\"3C=vq5*e([EF*$!33xh9W92')fF*7$$\"3'*>
%zo-'\\mBF*$!38V\"4(Rk5PdF*7$$\"3s/QS-s8)3#F*$!3Er-[:1k*[&F*7$$\"37$4q
v!\\.<=F*$!3=3+H]mBY_F*7$$\"3=$zo(Gv;r:F*$!3!>!zTn'4H-&F*7$$\"37'>.Hop
BK\"F*$!35\"p3(4Jz$z%F*7$$\"3[Le)4wR:2\"F*$!3K>\\['yL)eXF*7$$\"3#el(o#
HmTG)!#>$!3v!*)QxwKjK%F*7$$\"3#[+/@tb&feFX$!3yT!yDc%f)3%F*7$$\"3!)**)3
0cC?z$FX$!3y^4T*Gq+)QF*7$$\"3%4o[$fD-Y:FX$!3;mOY)H;fk$F*7$$!3%y9eX/b'e
h!#?$!3QJ2G.j)4T$F*7$$!3up(4&[Hf.EFX$!37'e)3vdG%=$F*7$$!3&Rz#RVNl?VFX$
!33P%)49htxHF*7$$!3Qh8u(R&*QC'FX$!34h:Pl4pIFF*7$$!3%RiyOf@Nw(FX$!3!)yk
L6Ml>DF*7$$!3+Z+$4L\"[#R*FX$!3mB[*4h=9F#F*7$$!3w!*4xS^!)p5F*$!3wroO17a
[?F*7$$!3uY_8*G8o>\"F*$!3Y3=:\"Hg(*z\"F*7$$!3ppI)e$zN+8F*$!3%p*)3qAPyb
\"F*7$$!3S\"Gvh$HO)Q\"F*$!3%3'>JV(H\"*H\"F*7$$!3Q!yFZ0^#\\9F*$!3CF]<P:
([0\"F*7$$!3u)4xA037\\\"F*$!3CT$Qb\\&))HyFX7$$!3i#GbzC5e]\"F*$!3ykqXb;
)y*[FX7$$!3EY#=ix&y\"\\\"F*$!34/DP0A#>C#FX7$$!3am6C!4YbW\"F*$\"3h)y^T&
3\"H^(Fgo7$$!3CMW57[0g8F*$\"3O!o:)*R!H**RFX7$$!3O^j5ia*\\B\"F*$\"3%f\"
Q;3OA_tFX7$$!3gEG6xlXq5F*$\"3K6'ogUu%y5F*7$$!3jZ%pu?LgJ)FX$\"3S'4$3FAO
%[\"F*7$$!3)3-([kZ)fg&FX$\"3wut@TsLu=F*7$$!31&)4wusd^?FX$\"3$zswFWa2K#
F*7$$\"3T?<4M'3s#=FX$\"3A[p%46Ibv#F*7$$\"3W**=A$Rj(ooFX$\"3-+MsO+2oKF*
7$$\"3cODdquaY7F*$\"3#)y+h*34.z$F*7$$\"3G@D=$\\^0$>F*$\"3'4Hzb/cHQ%F*7
$$\"3J%pYjJy'3FF*$\"3YO%y#RRR9]F*7$$\"3;J*\\%)4_Kl$F*$\"3uM7m!\\9wt&F*
7$$\"32'4vb2ZQq%F*$\"3z]\"31Y%*=]'F*7$$\"3%4ybM!fmQfF*$\"3k^6@;*y4O(F*
7$$\"3p$)eUa3&HM(F*$\"3[A512G4+$)F*7$$\"3'>d.O1gS0)F*$\"3Q(>1$)yBOw)F*
7$$\"3?%ecFt@)4))F*$\"3)oT'***R:*[#*F*7$$\"3Mc\\-^\"fSt*F*$\"3jI98aQWL
)*F*7$$\"3EDm[U1Ss5!#<$\"3d&RZ<]3]/\"F]z7$$\"3qS[Fz[%o;\"F]z$\"3,)RvJ#
)\\I5\"F]z7$$\"3%)zd>\"\\&=n7F]z$\"3Y[?KB*zR;\"F]z7$$\"354qC#*\\.\"Q\"
F]z$\"3NQ$>OO6BB\"F]z7$$\"3d8xXXLQ-:F]z$\"3)e5Y3bCVI\"F]z7$$\"3]'zN!4^
'fi\"F]z$\"3EV=y<[!pP\"F]z7$$\"3K[USo1Cd<F]z$\"3sFh$>vpKX\"F]z7$$\"3mV
-UbBR2>F]z$\"3j[,'f%Q!)R:F]z7$$\"3wh]3zE^n?F]z$\"3^;kp-+DJ;F]z-%'COLOU
RG6&%$RGBG$\"#5!\"\"$\"\"!F`]lF_]l-%+AXESLABELSG6$Q!6\"Fd]l-%%VIEWG6$%
(DEFAULTGFi]l" 1 2 0 1 10 0 2 9 1 4 1 1.000000 44.000000 43.000000 0 
0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "rsolve(\{y1(n+1)-4*y1(n)-y2(
n)=n^2,y2(n+1)+y1(n)-2*y2(n)=0\},\{y1(n),y2(n)\});" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#<$/-%#y1G6#%\"nG,0*(\"\"'!\"\")\"\"$F(\"\"\"F(F/F/*&
\"\")F,F-F/F,#F/F1F/*&\"\"%F,F(\"\"#F,*&#F/F.F/*(F-F/-F&6#\"\"!F/F(F/F
/F/*&F-F/F9F/F/*&F7F/*(F-F/-%#y2GF:F/F(F/F/F//-F@F',2*(F+F,F-F/F(F/F,*
(\"\"&F/F1F,F-F/F/*&F5F,F(F/F,#FFF1F,*&F4F,F(F5F,*&#F/F.F/F>F/F,*&F-F/
F?F/F/*&#F/F.F/F8F/F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "rs
olve(\{y1(n+1)-4*y1(n)-y2(n)=n^2,y2(n+1)+y1(n)-2*y2(n)=0,y1(0)=1,y2(0)
=0\},\{y1(n),y2(n)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%#y2G6#%
\"nG,,*(\"\"#!\"\")\"\"$F(\"\"\"F(F/F,*(\"\"&F/\"\")F,F-F/F/*&F+F,F(F/
F,#F1F2F,*&\"\"%F,F(F+F,/-%#y1GF',**(F+F,F-F/F(F/F/*(\"\"(F/F2F,F-F/F/
#F/F2F/*&F6F,F(F+F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "y1 := n -> 1/2*3^n*n+7/8*3^n
+1/8-1/4*n^2;\ny2 := n -> -1/2*3^n*n+5/8*3^n-1/2*n-5/8-1/4*n^2;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1Gf*6#%\"nG6\"6$%)operatorG%&arrow
GF(,**&#\"\"\"\"\"#F/*&)\"\"$9$F/F4F/F/F/*&#\"\"(\"\")F/F2F/F/#F/F8F/*
&#F/\"\"%F/*$)F4F0F/F/!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#y2Gf*6#%\"nG6\"6$%)operatorG%&arrowGF(,,*&#\"\"\"\"\"#F/*&)\"\"$9$F/
F4F/F/!\"\"*&#\"\"&\"\")F/F2F/F/*&#F/F0F/F4F/F5#F8F9F5*&#F/\"\"%F/*$)F
4F0F/F/F5F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for i fr
om 0 to 10 do print(y1(i),y2(i)); od;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$\"#;!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
\"#i!#G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"$H#!$=\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$\"$9)!$l%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"%;G
!%W<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"%c&*!%/j" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$\"&p>$!&k@#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"'wd5
!&(Hw" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"'))oM!'q$e#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 36 }{VIEWOPTS 
1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }