Answer: Use the Runge-Kutta for Systems Algorithm to approximate the solutions of the

Chapter 5, Problem 3

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Use the Runge-Kutta 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 2y 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 3y t 2y + 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. Copyright 2010 Cengage Le