Given the initial-value problem y' = y + t + 1, 0 t 5, y(0)
Question:
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.
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