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(a) Show that the system dx dt = y + xf(r) r , dy dt = ?

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(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

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(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 ? 6)2(r2 ? 6r + 5). Determine all periodic solutions and determine their stability characteristics

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