# Classification of Orbits

Describe the orbits of $$\frac{{\rm d}r}{{\rm d}t}=r(r-2)(r-4),$$ where $(r,t)$ is the usual polar co-ordinates.

Can we do solve this problem without integration? What is meant by 'describe' here? I am trying to use the Cantor-Bendixon Theorem , but I cannot really solve it.

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Hint: Think of it as a one-dimensional dynamical system, where $t$ is time, and draw the phase portrait on the $r$ axis. –  Hans Lundmark Sep 5 '12 at 14:27
Maybe this helps: W|A... –  draks ... Sep 5 '12 at 15:11