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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 98 "Maple Worksheet- Section 6.5 (This would only be for the graphs
, but you can also check your work)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "DE01:=diff(y(t),t$2)+2*dif
f(y(t),t)+2*y(t)=Dirac(t-Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 59 "Y01:=dsolve(\{DE01,y(0)=1,D(y)(0)=0\},y(t),method='laplace');" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(rhs(Y01),t=0..3*Pi);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "DE02:=diff(y(t),t$2)+4*
y(t)=Dirac(t-Pi)-Dirac(t-2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 59 "Y02:=dsolve(\{DE02,y(0)=0,D(y)(0)=0\},y(t),method='laplace');
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(rhs(Y02),t=0..4*Pi
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "DE03:=diff(y(t),t$2)+
3*diff(y(t),t)+2*y(t)=Dirac(t-5)+Heaviside(t-10);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 61 "Y03:=dsolve(\{DE03,y(0)=0,D(y)(0)=1/2\},y(t)
,method='laplace');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot
(rhs(Y03),t=0..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "DE04
:=diff(y(t),t$2)-y(t)=-20*Dirac(t-3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "Y04:=dsolve(\{DE04,y(0)=1,D(y)(0)=0\},y(t),method='la
place');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(rhs(Y04),t
=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "DE05:=diff(y(t)
,t$2)+2*diff(y(t),t)+3*y(t)=sin(t)+Dirac(t-3*Pi);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 59 "Y05:=dsolve(\{DE05,y(0)=0,D(y)(0)=0\},y(t),m
ethod='laplace');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(r
hs(Y05),t=0..14);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "DE06:=
diff(y(t),t$2)+4*y(t)=Dirac(t-4*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "Y06:=dsolve(\{DE06,y(0)=1/2,D(y)(0)=0\},y(t),method='
laplace');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(rhs(Y06)
,t=0..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "DE08:=diff(y(
t),t$2)+4*y(t)=2*Dirac(t-Pi/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 59 "Y08:=dsolve(\{DE08,y(0)=0,D(y)(0)=0\},y(t),method='laplace');
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(rhs(Y08),t=0..8);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
90 "Problems 17-21.  In this case, we'll need a short loop to construc
t the sum of Heavisides:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "H17:=0;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 53 "for k from 1 to 20 do H17:=H17+Dirac(t-k*Pi): end d
o:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "DE17:=diff(y(t),t$2)+
y(t)=H17;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Y17:=dsolve(\{
DE17,y(0)=0,D(y)(0)=0\},y(t),method='laplace');" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "plot(rhs(Y17),t=0..20);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 7 "H19:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 55 "for k from 1 to 20 do H19:=H19+Dirac(t-k*Pi/2): end do:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "DE19:=diff(y(t),t$2)+y(t)=H1
9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Y19:=dsolve(\{DE19,y(
0)=0,D(y)(0)=0\},y(t),method='laplace');" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "plot(rhs(Y19),t=0..40);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "H20:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "
for k from 1 to 20 do H20:=H20+Dirac(t-k*2*Pi): end do:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "DE20:=diff(y(t),t$2)+y(t)=H20;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Y20:=dsolve(\{DE20,y(0)=0,D(
y)(0)=0\},y(t),method='laplace');" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "plot(rhs(Y20),t=0..60);" }}}{EXCHG {PARA 0 "> " 0 "" 
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