(a) Show that the system dx/dt = y + xf(r)/r, dy/dt = x + yf(r)/r has periodic solutions

Chapter 9, Problem 8

(choose chapter or problem)

(a) Show that the system dx/dt = y + xf(r)/r, dy/dt = x + yf(r)/r has periodic solutions corresponding to the zeros of f(r). What is the direction of motion on the closed trajectories in the phase plane? (b) Let f(r) = r(r 2)2(r2 4r + 3). Determine all periodic solutions and determine their stability characteristics

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