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Convince yourself in the fact that for any 0 the solution of the van der Pol's equation with the initial conditions x(0) = 2 ,

  1. Convince yourself in the fact that for any 0 the solution of the van der Pol's equation with the initial conditions x(0) = 2 , x(0) = 0 is periodic. For this translate the IVP into the corresponding IVP for the system and solve it by Euler's method with the step-size h = 0.05for = 0 , 1.5, and 3 . Sketch the corresponding trajectories on the phase-plane. Supply the table of the first 20 values of x(t) and x(t)of your numerical solutions in each case = 0 , 1.5, and 3 .Estimate the period of the periodic solutions for = 0 , 1.5, and 3 .

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