Construct an AdamsVariable Step-Size Predictor-Corrector Algorithm based on the Adams-Bashforth five-step method and the Adams-Moulton four-step method. Repeat Exercise 3 using this newmethod.

In Exercise 3

a. y' = y/t − (y/t)², 1≤ t ≤ 4, y(1) = 1; actual solution y(t) = t/(1 + ln t).

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

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

d. y' = (t + 2t³)y³ − ty, 0≤ t ≤ 2, y(0) = 1/3 ; actual solution y(t) = (3 + 2t² + 6(e^t)²)^−1/2.