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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 33 "One Dimensional Plot of
 Solutions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart:\nwit
h(plots):\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "Def
ine the differential equation using parameters:\nFor a different equat
ion, you will have to change the ODE." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "r:= 1; K:= 1;\nODE := [diff(x(t),t) = r*x(t)*(K-x(t))
/K];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Next pick the initial con
ditions which show the important features of the equation." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "IC:=[[x(0)=2],[x(0)=1],[x(0)=0.1],[
x(0)=0],[x(0)=-0.1]];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 141 "Plot t \+
versus x.  \nNote: for a different ODE, you will probably have to chan
ge the range of x displayed.  \n(Here the range is from -1 to 2.) " }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "DEplot(ODE, [x(t)], t=0..5
,  \nIC,linecolour=BLUE, x=-1..2, stepsize=0.1,\narrows=NONE, method=c
lassical[rk4],scene=[t,x]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Pl
ot the vector field for T' =1 and   x' = r x(K-x)/K" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 52 "fieldplot([1,r*x(t)*(K-x(t))/K], T=0..5, \+
x = -1..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
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