Exercise 45: Consider the differential equation for the Van der Pol oscillator (use a RK4 integrator) :5} + 6(32 1)?) + y = 0 which has a nonlinear damping term ((3,:2 1);}. (a) write this ODE as a system of rst order differential equations. (b) Analyze the stability of the xed point at y = 3} = [l for e > 0. (c) For e = 0.1, solve the equation for t=0:0. 1 :30 for initial conditions MD) 2 [1.1 and 9(0) 2 1. Repeat for e = 1 and E = 20. Plot the phase portrait (3'; vs. 3)) for each of the three cases to see the various behaviors