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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "LaplaceClass_A11.mws\nTue \+
Oct 11 09:20:59 MDT 2005\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "with(plots, display):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "step := (t,A) -> Heaviside(t-A);  " }{TEXT -1 27 "Our
 text's \"step\" function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
47 "RHS := t -> (1 - step(t,1))*2*t + 2*step(t,1); " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "TRG := 0..4:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "P_RHS := plot(RHS, TRG): " }{TEXT -1 37 "Save drivi
ng-function plot for later." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "#display(P_RHS);  " }{TEXT -1 52 "Checking if the driving function
's entered properly." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 70 "The differential equation: y'' +  y = RHS with \+
y(0) = 0 and y'(0) = 1." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "DEA := (D@@2)(y)(t) + y(t) = RHS(t)
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
30 "Set up the initial conditions:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "WIMPY := y(0) = 0, D(y)(0) \+
= 1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 48 "Put together the argument sequence for \"dsolve\":" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "IVP \+
:= \{DEA, WIMPY\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "VARS \+
:= y(t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "CARGO := IVP, V
ARS:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "SOLN := dsolve(CARG
O);  " }{TEXT -1 32 "Solve the initial-value problem." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Recover t
he solution for plotting and checking:" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "yy := unapply( rhs(SOLN
), t):  " }{TEXT -1 33 "Get solution as Maple function yy" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "P_SOLN := plot(yy, TRG, colour=BLAC
K):  " }{TEXT -1 18 "Plot the solution." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "display(P_RHS, P_SOLN);  " }{TEXT -1 39 "Solution and
 driving function together." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
56 "########################################################" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "He
re we check the piecewise formula for the solution:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "assume(u \+
< 1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assume(v > 1);  " 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "yy(u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "yy(v);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "##############
###########################################" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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