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

Chapter 5, Problem 3

(choose chapter or problem)

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 = ?c' ?, 0 < ? < 1, y(0) = y'(0) = 0, with h =0.1; actual solution y(?) = i?3 c' - ?c' + 2c' - ? - 2. b. t 2 y" - 2ty' + 2y = t 3 In t, 1 < ? < 2, y(l) = I, y'(l) = 0, with h = 0.1; actual solution y(?) = |? + T?3 in? - |?3 . c. y'"+ 2y" - y'-2y = e', 0 < ? < 3, y(0) = 1, y'(0) = 2, y"(0) = 0, with/? = 0.2; actual solution y(?) = ||c' + ^e~' - p~2 ' + i?c'. d. ? 3 y"' ? 2 y" + 3?y' 4y = 5?3 In? + 9?3 , 1 < ? < 2, y(l) = 0, y'(l) = 1, y"(l) = 3, with h =0.1; actual solution y(?) = -?2 + ? cos(ln ?) + ? sin(ln?) + ? 3 In?