Before any of the special differential equations package commands, you need
to type:
> with(DEtools):
To plot a slope field for a differential equation:
> DEplot(diff(y(x),x)=1/(x^2-1),y(x),x=-2..2,y=-2..2);
or:
> DEplot(diff(p(t),t)=-p*(p-2.5),p(t),t=0..5,p=0..5);
or:
> DEplot(diff(p(t),t)=-p*(p-4)*(p-5),p(t),t=0..5,p=0..6);
To plot a slope field for a differential equation along with a solution
curve satisfying an initial condition:
> DEplot(diff(p(t),t)=-p*(p-4)*(p-5),p(t),t=0..5,p=0..6,
[[p(0)=3]]);
or for better approximations (less jaggedness, but slower plotting):
> DEplot(diff(p(t),t)=-p*(p-4)*(p-5),p(t),t=0..5,p=0..6,
[[p(0)=3]], stepsize=0.005);
To plot the phase plane for a system of two differential equations:
> DEplot( {diff(R(t),t)=2*R(t)-1.2*R(t)*F(t),
diff(F(t),t)=-F(t)+.9*R(t)*F(t)} , [R(t), F(t)], t=0..3, R=0..3,F=0..3, arrows=LARGE);
To plot the phase plane for a system of two differential equations, including
a solution curve satisfying an initial condition:
> DEplot( {diff(R(t),t)=2*R(t)-1.2*R(t)*F(t),
diff(F(t),t)=-F(t)+.9*R(t)*F(t)} , [R(t), F(t)], t=0..5, R=0..3,F=0..3, arrows=LARGE,
[[R(0) = 1, F(0) = 1]]);
To plot the phase space for a system of three differential
equations, including a solution curve satisfying an initial condition:
> DEplot3d( {diff(R(t),t)=-.2*R(t)-.04*R(t)*M(t)+.0008*R(t)*P(t),
diff(M(t),t)=-.1*M(t) +.01*R(t)*M(t), diff(P(t),t)=2*P(t)-.002*(P(t))^2-.1*R(t)*P(t)}
, [R(t), M(t), P(t)], t=0..100, R=0..20,M=0..20,P=0..1000, [[R(0) = 20, M(0)
= 1, P(0)=600]], stepsize=0.5);
A chaotic system (vary the range of t values and/or
initial conditions to see this):
> DEplot3d( {diff(x(t),t)=10*(y(t)-x(t)), diff(y(t),t)=28*x(t)-y(t)-x(t)*z(t),
diff(z(t),t)=-8/3*z(t)+x(t)*y(t)} , [x(t), y(t), z(t)], t=0..6, [[x(0) =
10, y(0) = 10, z(0)=30]], stepsize=0.01);