> with(DEtools):

A plot similar to Figure 1.5.3 on page 41 of our text, where we show the height (in meters) of a whiffle ball subject to air resistence, using k/m = 3, and initial velocities 5 and 15 meters per second, as a system:

> DEplot([diff(y(t),t)=v(t), diff(v(t),t)=-9.8-3*v(t)],
[y(t),v(t)],t=0..2.5,y=0..5,[[y(0)=0,v(0)=15],[y(0)=0,v(0)=5]],
method=rkf45,stepsize=.05,scene=[t,y],linecolor=black);

Same thing, but as a second order single differential equation. Note the peculiar way we give the initial condition y'(0) = 15 etc.

> DEplot([diff(y(t),t,t)=-9.8-3*diff(y(t),t)],
[y(t)],t=0..2.5,y=0..5,[[y(0)=0,D(y)(0)=15],[y(0)=0,D(y)(0)=5]],
method=rkf45,stepsize=.05,linecolor=black);

A plot similar to Figure 1.5.4, with k/m = 10, and using the sequence command to quickly generate many initial conditions.

> DEplot([diff(y(t),t)=v(t), diff(v(t),t)=-9.8-10*v(t)],
[y(t),v(t)],t=0..2.5,y=0..2,
[seq([y(0)=0,v(0)=5*k],k=1..4)],
method=rkf45,stepsize=.05,scene=[t,y],linecolor=aquamarine);

Differential Equations Materials Page.