Use Taylor's method of order two to approximate the solution for each of the following initial-value problems.

Question:

Use Taylor's method of order two to approximate the solution for each of the following initial-value problems.
a. y' = y/t − (y/t)2, 1≤ t ≤ 1.2, y(1) = 1, with h = 0.1
b. y' = sin t + e−t, 0≤ t ≤ 1, y(0) = 0, with h = 0.5
c. y' = (y2 + y)/t, 1≤ t ≤ 3, y(1) = −2, with h = 0.5
d. y' = −ty + 4ty−1, 0≤ t ≤ 1, y(0) = 1, with h = 0.25