Phase portraits of ODEs?

Has anyone out there used Igor to make a phase portrait (aka phase space plot) of an ODE? I attach an example (middle plot) below. The general idea is to plot representative solutions of a specified 2-dimensional ODE (here, a pendulum with damping), to illustrate various cases of motion (here, back-and-forth swinging and end-over-end motion).

I have looked but not found any pre-packaged examples. In principle, this is not hard -- one just has to integrate ODEs and plot trajectories, but you need to pick the "right" set of trajectories (i.e. initial conditions) to make the result look good. This can be a lot of work, and it would be much easier to start from a working code.