Hi, all above should correct in on. The matlab code. Problem 3. The equationdt2x(t) = − x(t) + µ(1 − x(t)²) = x(t)known as the Van der Pol equation, represents a simple oscillator.a. Reduce the Van der Pol equation to a system of first-order ODES.b. Implement forward Euler, backward Euler and the trapezoidal schemes for the solution of the Vander Pol oscillator.c. Use your implementations from part (b) to generate solutions for the Van der Pol oscillator for μ = 1and μ = 10. Use x(0) = 2, ż(0) = 0 and experiment with various step sizes to obtain reasonableaccuracy for each value of u with all of the schemes you implemented in part (b). Compute the solutionin the time interval t = [0, max(20, 10μ)].Comment on your results.

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Hi, all above should correct in on. The matlab code.

Problem 3. The equation
dt2x(t) = − x(t) + µ(1 − x(t)²) = x(t)
known as the Van der Pol equation, represents a simple oscillator.
a. Reduce the Van der Pol equation to a system of first-order ODES.
b. Implement forward Euler, backward Euler and the trapezoidal schemes for the solution of the Van
der Pol oscillator.
c. Use your implementations from part (b) to generate solutions for the Van der Pol oscillator for μ = 1
and μ = 10. Use x(0) = 2, ż(0) = 0 and experiment with various step sizes to obtain reasonable
accuracy for each value of u with all of the schemes you implemented in part (b). Compute the solution
in the time interval t = [0, max(20, 10μ)].
Comment on your results.

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