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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Brief Maple demonstration \+
for the solution of ODEs\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "restart: with(DEtools): with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 
50 "Warning, the name changecoords has been redefined\n" }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT 258 51 "Analytical and Numerical Solutions, Dire
ction Field" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f1 := x -> 3 \+
- x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "de1 := diff(x(t),t)
 = f1(x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sol1 := dso
lve(de1,x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ic1 := x(
0) = 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sol1a := rhs(dso
lve(\{de1,ic1\},x(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "
plot(sol1a,t=0..5);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "dfieldplo
t(de1,x(t),t=0..8,x=-1..5,arrows=SLIM);" }}{PARA 13 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "DEplot(de1,x(t),t=0.
.8,x=-1..5);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 38 "icset1 := [seq([x(0)=i+0.3],i=-1..4)];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "DEplot(de1,x(t),t=0..8,x=-1.
.5,icset1,stepsize=0.1,linecolor=black);" }}{PARA 13 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?DEplot" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT 257 17 "Logistic Equation" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 42 "logeq := diff(N(t),t) = r*N(t)*(1-N(t)/K);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "loginit := N(0) = N0;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "logsoln := dsolve(\{logeq,lo
ginit\},N(t));" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 26 "r := 1; K := 4; N0 := 0.2;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 7 "K := 4;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "plot(rhs(logsoln),t=0..20);" }}{PARA 13 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dfieldplot(
logeq,N(t),t=0..10,N=-2..6,arrows=SLIM);" }}{PARA 13 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "DEplot(logeq,N(t),t=
0..20,N=-2..6);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 34 "iniset := [seq([N(0)=i],i=-1..5)];" }}{PARA 
12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "
DEplot(logeq,N(t),t=0..10,N=-2..6,iniset,stepsize=0.1,linecolor=black)
;" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}}{MARK "3" 0 }{VIEWOPTS 1 1 0 
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