Consider the initial value problemy= 10y + 2.5t2 + 0.5t,

Chapter 8, Problem 4

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Consider the initial value problemy= 10y + 2.5t2 + 0.5t, y(0) = 4.(a) Find the solution y = (t) and draw its graph for 0 t 5.(b) The stability analysis in the text suggests that for this problem, the Euler method isstable only for h < 0.2. Confirm that this is true by applying the Euler method to thisproblem for 0 t 5 with step sizes near 0.2.(c) Apply the RungeKutta method to this problem for 0 t 5 with various step sizes.What can you conclude about the stability of this method?(d) Apply the backward Euler method to this problem for 0 t 5 with various stepsizes. What step size is needed to ensure that the error at t = 5 is less than 0.01?