Given the initial-value problem

y' = −y + t + 1, 0 ≤ t ≤ 5, y(0) = 1,

With exact solution y(t) = e^−t + t:

a. Approximate y(5) using Euler’s method with h = 0.2, h = 0.1, and h = 0.05.

b. Determine the optimal value of h to use in computing y(5), assuming δ = 10−6 and that Eq. (5.14) is valid.