Consider the initial value problem (y' (t) = 2(t- y) +1, 0≤ t ≤ 2 ly(0) = 1, for which the exact solution is y(t) = e-²t + t. (a) Show that this IVP is well-posed on D = {(t,y)|0 ≤ t ≤ 2, -∞ < y<∞0}. (b) Using the error bound at t = 2, hM YN - YN ≤ -[e¹(b-a) – 1] 2L where yN = y(2), YN is the numerical approximation to y(2), L is the Lipschitz constant, M = max ly"(t)], and [a, b] = [0,2], find the value of h necessary for the error to be at most 10-5. Ost≤2

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