{VERSION 5 0 "IBM INTEL LINUX" "5.0" }
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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 32 "Phase Portrait for Line
ar System" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 
"restart:\nwith(plots):\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 50 "Define the differential equation using parameters:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "a:=1:b:=3:c:=3:d:=1: \nLinD
E := [diff(x(t),t) = a*x(t)+b*y(t),\n          diff(y(t),t) = c*x(t)+d
*y(t)];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 121 "Plot the phase portra
it using Runge-Kutta method;  the initial conditions are given in the \+
first line and can be changed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 169 "IC1:=[[x(0)=-2,y(0)=2],[x(0)=2,y(0)=-2],[x(0)=0.01,y(0)=0.01]
,\n  [x(0)=-0.01,y(0)=-0.01],[x(0)=-1.9,y(0)=2],[x(0)=1.9,y(0)=-2],\n \+
 [x(0)=-2,y(0)=1.9],[x(0)=2,y(0)=-1.9]];" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 147 "DEplot(LinDE, [x(t),y(t)], t=-1.7..1.8,  \n  IC1,lin
ecolour=BLUE, x=-2..2, y=-2..2, stepsize=0.1,\n  arrows=NONE, method=c
lassical[rk4],scene=[x,y]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Yo
u could try changing the parameters in the equation to get different e
xamles. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 15 "Plot x versus t" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "IC2:=[[x(0)=2,y(0)=-2]];" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 144 "DEplot(LinDE, [x(t),y(t)], t=0..1.7,  \n  IC2
,linecolour=BLUE, x=-1..2, y=-2..2, stepsize=0.1,\n  arrows=NONE, meth
od=classical[rk4],scene=[t,x]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }
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