Use each of the Adams-Bashforth methods to approximate the solutions to the following initial-value problems. In each case use starting values obtained from the Runge-Kutta method of order four. Compare the results to the actual values.
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 = 0.1; 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 .