Repeat Exercise 2 using the Runge-Kutta method of order four.

In Exercise 2

a. y' = e^t−y, 0≤ t ≤ 1, y(0) = 1, with h = 0.5; actual solution y(t) = ln(e^t + e − 1).

b. y' = (1 + t)/(1 + y), 1≤ t ≤ 2, y(1) = 2, with h = 0.5; actual solution y(t) =√(t² + 2t + 6−1).

c. y' = −y + ty^1/2, 2 ≤ t ≤ 3, y(2) = 2, with h = 0.25; actual solution y(t) =(t − 2 +√2ee^−t/2)².

d. y' = t⁻²(sin 2t − 2ty), 1 ≤ t ≤ 2, y(1) = 2, with h = 0.25; actual solution y(t) =1/2 t⁻²(4 + cos 2 − cos 2t).