System (4.63) can be solved exactly. Integrate the \(r\)-equation using separation of variables. For initial conditions

(a) \(r(0)=0.25, \theta(0)=0\), and

(b) \(r(0)=1.5, \theta(0)=0\), and \(\mu=1.0\), find and plot the solutions in the \(x y\)-plane, showing the approach to a limit cycle.

Data from 4.63

r-r, 0' = 1.