Use the Extrapolation Algorithm with tolerance TOL = 104, hmax = 0.25, and hmin = 0.05

Chapter 5, Problem 5.8.1

(choose chapter or problem)

Use the Extrapolation Algorithm with tolerance TOL = 104, hmax = 0.25, and hmin = 0.05 to approximate the solutions to the following initial-value problems. Compare the results to the actual values. a. y = te3t 2y, 0 t 1, y(0) = 0; actual solution y(t) = 1 5 te3t 1 25 e3t + 1 25 e2t . b. y = 1 + (t y)2, 2 t 3, y(2) = 1; actual solution y(t) = t + 1/(1 t). c. y = 1 + y/t, 1 t 2, y(1) = 2; actual solution y(t) = t ln t + 2t. d. y = cos 2t + sin 3t, 0 t 1, y(0) = 1; actual solution y(t) = 1 2 sin 2t 1 3 cos 3t + 4 3 .