Repeat Exercise 4 using the Midpoint method.

In Exercise 4

a. y' = (2 − 2ty)/(t² + 1), 0≤ t ≤ 1, y(0) = 1, with h = 0.1; actual solution y(t) = (2t + 1)/(t² + 1).

b. y' = y²/(1 + t), 1≤ t ≤ 2, y(1) = −(ln 2)⁻¹, with h = 0.1; actual solution y(t) =−1/(ln(t + 1)).

c. y' = (y² + y)/t, 1≤ t ≤ 3, y(1) = −2, with h = 0.2; actual solution y(t) = 2t/(1 − 2t).

d. y' = −ty + 4t/y, 0≤ t ≤ 1, y(0) = 1, with h = 0.1; actual solution y(t) =√((4 − 3e^−t)².)