Use Taylor's method of order two to approximate the solutions for each of the following initial-value problems.
a. y' = et−y, 0≤ t ≤ 1, y(0) = 1, with h = 0.5
b. y' = (1 + t)/(1 + y), 1≤ t ≤ 2, y(1) = 2, with h = 0.5
c. y' = −y + ty1/2, 2≤ t ≤ 3, y(2) = 2, with h = 0.25
d. y' = t−2(sin 2t − 2ty), 1≤ t ≤ 2, y(1) = 2, with h = 0.25