Use all the Adams-Moulton methods to approximate the solutions to the Exercises 1(a), 1(c), and 1(d). In each case use exact starting values, and explicitly solve for wi+1. Compare the results to the actual values.
In Exercise 1
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).
c. y' = −(y + 1)(y + 3), 0 ≤ t ≤ 2, y(0) = −2, with h = 0.1; actual solution y(t) = −3 + 2/(1 + e−2t).
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).