This problem involves the default system in pplane6, i.e., the planar system that appears when pplane6 is first started.
a) Find and plot all interesting features, i.e., equilibrium points, separatrices, limit cycles, and any other features that appeal to you. Make a list of such to turn in with the plot.
b) Find the linearization of the system at (0,0). Enter that into pplane6 and plot a few orbits.
c) Go back to the default system. According to theory, the linearization should approximate the original system in a small enough neighborhood of (0,0). Use the Zoom in sqnare option to find a small enough rectangle containing (0, 0), where the behavior of the system is closely approximated by the linear system you analyzed in part b).
d) Redo parts b) and c) for the other equilibrium points of the default system.
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