Solved: Use the RungeKutta for Systems Algorithm to approximate the solutions of the

Chapter 5, Problem 5.9.3

(choose chapter or problem)

Use the RungeKutta for Systems Algorithm to approximate the solutions of the following higherorder differential equations, and compare the results to the actual solutions. a. y 2y + y = tet t, 0 t 1, y(0) = y (0) = 0, with h = 0.1; actual solution y(t) = 1 6 t 3et tet + 2et t 2. b. t 2 y 2ty + 2y = t 3 ln t, 1 t 2, y(1) = 1, y (1) = 0, with h = 0.1; actual solution y(t) = 7 4 t + 1 2 t 3 ln t 3 4 t 3. c. y + 2y y 2y = et , 0 t 3, y(0) = 1, y (0) = 2, y(0) = 0, with h = 0.2; actual solution y(t) = 43 36 et + 1 4 et 4 9 e2t + 1 6 tet . d. t 3 y t 2 y + 3ty 4y = 5t 3 ln t + 9t 3, 1 t 2, y(1) = 0, y (1) = 1, y(1) = 3, with h = 0.1; actual solution y(t) = t 2 + t cos(ln t) + t sin(ln t) + t 3 ln t.