The driven Van der Pol equation is a second order nonlinear differential equation which may be expressed as two first order differential equations as follows, with a driving force of amplitude F and period Tdr

dx₁/dt = x₂

dx₂/dt - e(1 - x₁²)x₂ + x₁ = Fcos(2t/T)

The solutions of this system has a stable limit cycle (periodic) solution, which means that if you plot the phase trajectory of the solution (the plot of x₁ against x₂) starting at any point in the positive x₁ vs x₂ plane, it always moves continuously into the same closed loop. Use ode23 in MatLab to solve this system numerically for x₁(0) = 0 and x₂(0) = 1. Draw phase trajectories for e = 6 for F = 1.2 and Tdr = 10 and see if this solution is periodic.