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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 11 "Math 2280-2" }}{PARA 257 "" 0 "
" {TEXT -1 21 "Friday 23 March, 2001" }}{PARA 258 "" 0 "" {TEXT -1 57 
"Inhomogeneous linear systems of differential equations - " }}{PARA 
259 "" 0 "" {TEXT -1 64 "methods of undetermined coefficients and vari
ation of parameters" }}{PARA 0 "" 0 "" {TEXT -1 27 "Work for example 2
 page 368" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "A:=matrix(3,3,[-.5,0,0,.5
,-.25,0,0,.25,-.2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matri
xG6#7%7%$!\"&!\"\"\"\"!F-7%$\"\"&F,$!#D!\"#F-7%F-$\"#DF3$F3F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6%7%$!\"&!\"\"\"\"\"<#-%'vectorG6#7%F'$!+++++?!\"*
$\"+nmmm;F/7%$!#D!\"#F'<#-F*6#7%\"\"!F'$!+++++]F/7%$F5F&F'<#-F*6#7%F:F
:F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "k:=evalm(inverse(A)&
*vector([-20,0,0]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG-%'vecto
rG6#7%$\"+++++S!\")$\"+++++!)F+$\"+++++5!\"(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 40 "Phi0:=matrix(3,3,[3,0,0,-6,1,0,5,-5,1]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Phi0G-%'matrixG6#7%7%\"\"$\"\"!F+7%
!\"'\"\"\"F+7%\"\"&!\"&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
28 "c:=evalm(-inverse(Phi0)&*k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"cG-%'vectorG6#7%$!+LLLL8!\")$!+++++;!\"($!+LLLL$)F." }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Work for example 4 page 3
72" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "A:=matrix(2,2,[4,2,3,-
1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7$\"\"%\"
\"#7$\"\"$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x0:=vect
or([7,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G-%'vectorG6#7$\"\"
(\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "f:=t->evalm(-t*ex
p(-2*t)*vector([15,4]));\n#the inhomogeneous term." }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fGR6#%\"tG6\"6$%)operatorG%&arrowGF(-%&evalmG6#,$
*(9$\"\"\"-%$expG6#,$F1!\"#F2-%'vectorG6#7$\"#:\"\"%F2!\"\"F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "sol:=t->evalm(exponential(A
,t)&*(x0+\nint(exponential(-A,s)&*f(s),s=0..t)));\n#solution formula i
n Maple" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solGR6#%\"tG6\"6$%)opera
torG%&arrowGF(-%&evalmG6#-%#&*G6$-%,exponentialG6$%\"AG9$,&%#x0G\"\"\"
-%$intG6$-F06$-F36$,$F5!\"\"%\"sG-%\"fG6#FC/FC;\"\"!F6F9F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sol(t);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#-%'vectorG6#7$,&*&,&-%$expG6#,$%\"tG!\"##\"\"\"\"\"(*&#
\"\"'F2F1-F+6#,$F.\"\"&F1F1F1,&F2F1*&#F1\"#9F1*&,*F.!#G\"\"%!\"\"*(F2F
1)F.\"\"#F1)-F+6#F.F2F1F1*&FAF1FFF1F1F1*$FFF1FBF1FBF1F1*&,&F6#FEF2*&#F
EF2F1F*F1FBF1,&\"\"$F1*&*&#F1F=F1,**&FDF1FFF1\"#@*&F=F1F.F1F1FEF1*&FEF
1FFF1FBF1F1*$FFF1FBF1F1F1,&*&,&F6#FQF2*&#FQF2F1F*F1FBF1F:F1F1*&,&F*F4*
&F0F1F6F1F1F1FPF1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "simp
lify(%);\n#this is the solution at the bottom of page 372" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$,*-%$expG6#,$%\"tG!\"##\"\"$\"\"(
*&#\"\"\"\"\"#F3*&F(F3)F,F4F3F3!\"\"*&#\"#YF0F3-F)6#,$F,\"\"&F3F3*(F4F
3F(F3F,F3F3,*F;#\"#BF0*&F(F3F,F3F3*&#F4F0F3F(F3F7*(#F/F4F3F(F3F6F3F3" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0" 41 }
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