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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 14 "Example 1.06.1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "ode1 := diff(s(t),t,t) + 6*diff(s(t),t) + 9*s(t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G,(-%%diffG6$-%\"sG6#%\"tG-%\"$
G6$F,\"\"#\"\"\"*&\"\"'F1-F'6$F)F,F1F1*&\"\"*F1F)F1F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ics1 := s(0) = 1, D(s)(0) = 0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ics1G6$/-%\"sG6#\"\"!\"\"\"/--%\"DG
6#F(F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dsolve(\{ode1,i
cs1\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"sG6#%\"tG,&-%$expG6#,$
*&\"\"$\"\"\"F'F/!\"\"F/*(F.F/F)F/F'F/F/" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 14 "Example 1.07.1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
66 "ode1 := diff(x(t),t,t) + 2*diff(x(t),t) + 26*x(t) = 10*Dirac(t-3);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,(-%%diffG6$-%\"xG6#%\"tG
-%\"$G6$F-\"\"#\"\"\"*&F1F2-F(6$F*F-F2F2*&\"#EF2F*F2F2,$*&\"#5F2-%&Dir
acG6#,&F-F2\"\"$!\"\"F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "ics1 := x(0) = 0, D(x)(0) = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%%ics1G6$/-%\"xG6#\"\"!F*/--%\"DG6#F(F)F*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "dsolve(\{ode1,ics1\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%\"xG6#%\"tG,$**\"\"#\"\"\"-%*HeavisideG6#,&F'F+\"\"$
!\"\"F+-%$expG6#,&F'F1F0F+F+-%$sinG6#,&\"#:F1*&\"\"&F+F'F+F+F+F+" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Example 1.07.2 and 1.08.1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "ode1 := diff(y(x),x,x) + 2*d
iff(y(x),x) - 3*y(x) = x^2 + exp(2*x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%ode1G/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"*&F1F2-F(
6$F*F-F2F2*&\"\"$F2F*F2!\"\",&*$)F-F1F2F2-%$expG6#,$*&F1F2F-F2F2F2" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dsolve(ode1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,.*&-%$expGF&\"\"\"%$_C2GF,F,*&-F+
6#,$*&\"\"$F,F'F,!\"\"F,%$_C1GF,F,*&F3F4F'\"\"#F4*(\"\"%F,\"\"*F4F'F,F
4#\"#9\"#FF4*&#F,\"\"&F,-F+6#,$*&F7F,F'F,F,F,F," }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 14 "Example 1.08.2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "ode1 := diff(y(x),x,x) + 4*diff(y(x),x) + 4*y(x) = ex
p(-2*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,(-%%diffG6$-%\"y
G6#%\"xG-%\"$G6$F-\"\"#\"\"\"*&\"\"%F2-F(6$F*F-F2F2*&F4F2F*F2F2-%$expG
6#,$*&F1F2F-F2!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dsol
ve(ode1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,(*&-%$expG
6#,$*&\"\"#\"\"\"F'F0!\"\"F0%$_C2GF0F0*(F*F0F'F0%$_C1GF0F0*&#F0F/F0*&)
F'F/F0F*F0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(intt
rans):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Example 1.09.1 (part)" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "invlaplace((a*s+4*a+b)/(s
+2)^2 + 1/(s+2)^3,s,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"
\"\"#F&*&-%$expG6#,$*&F'F&%\"xGF&!\"\"F&,(*&F'F&%\"aGF&F&*$)F.F'F&F&*(
F'F&,&*&F'F&F2F&F&%\"bGF&F&F.F&F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 21 "Example 1.09.2 (part)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "invlaplace(10*exp(-3*s)/(s^2+2*s+26),s,t);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#\"\"\"-%*HeavisideG6#,&%\"tGF&\"\"$
!\"\"F&-%$expG6#,&F+F-F,F&F&-%$sinG6#,&\"#:F-*&\"\"&F&F+F&F&F&F&" }}}
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