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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 41 "Phase Portrait for the \+
nonlinear equation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "resta
rt:\nwith(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 189 "What you will want to change
 for a different problem, is (i) the definition of the differential eq
uation, given in the line defining NonLinDE, (ii) the initial conditio
ns, given in the line" }}{PARA 0 "" 0 "" {TEXT -1 101 "defining IC, an
d (iii) the range of the varariables x and y, and the range of time t \+
in the line for " }}{PARA 0 "" 0 "" {TEXT -1 175 "the plot of the phas
e portrait (x=-2..2, y=-2..2, t=-7..6).  Sometimes you may want to adj
ust the step size in the plot of the phase protrait to a number betwee
n 0.1 and 0.01." }}{PARA 0 "" 0 "" {TEXT -1 55 "The following line def
ines the differential equation.  " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 81 "NonLinDE := [diff(x(t),t) = -x(t)+y(t),\n            \+
 diff(y(t),t) = x(t)*y(t)-1];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 
"Plot the phaseportrait using Runge-Kutta method;  the initial conditi
ons are given in the first line and can be changed." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 188 "IC:=[[x(0)=1.01,y(0)=1.022],[x(0)=1.1,y(
0)=2],[x(0)=1.6,y(0)=2],\n  [x(0)=-2,y(0)=1],[x(0)=0.99,y(0)=1-0.022],
[x(0)=2,y(0)=0.61],        [x(0)=1,y(0)=-1],[x(0)=0,y(0)=0],[x(0)=-2,y
(0)=-1]];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "DEplot(NonLinDE, [x(t
),y(t)], t=-7..6,  \n  IC,linecolour=BLUE, x=-2..2, y=-2..2, stepsize=
0.1,\n  arrows=NONE, method=classical[rk4]);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 34 "Plot one coordinate versus time.  " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 32 "IC2:=[[x(0)=0.99,y(0)=1-0.022]];" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 147 "DEplot(NonLinDE, [x(t),y(t)], t=0..5,  \n \+
 IC2,linecolour=BLUE, x=0.25..2, y=0..2, stepsize=0.02,\n  arrows=NONE
, method=classical[rk4],scene=[t,x]);" }}}{EXCHG {PARA 0 "> " 0 "" 
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