Repeat Exercise 3 using Heun’s method.

In Exercise 3

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

b. y' = 1+y/t +(y/t)², 1≤ t ≤ 3, y(1) = 0, with h = 0.2; actual solution y(t) = t tan(ln t).

c. y' = −(y + 1)(y + 3), 0 ≤ t ≤ 2, y(0) = −2, with h = 0.2; actual solution y(t) = −3 + 2(1 + e−2t)⁻¹.

d. y' = −5y+5t²+2t, 0≤ t ≤ 1, y(0) = 1/3 , with h = 0.1; actual solution y(t) = t²+ 1/3 e^−5t .