Approximate the solution of dy y(x + 1) dx x3 + x2 – 2x at x = 2 for the initial value problem y(1.1)=0.5 using (a) Euler method, (b) Improved Euler method and (c) 4th order Runge-Kutta method. Compare the estimated values obtained using the different methods with the exact value by computing the % difference. Use a step size, h = 0.1. Show the sample calculations for the first and last iterations only. Use the provided table to present the summary of calculated values. Round up your answers to six decimal places.

Q: Approximate the solution of dy y(x + 1) dx x3 + x2 - 2x at x = 2 for the initial value problem…

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