Consider the initial value problem y__ + y = f (t), y(0) = 0, y_(0) = 0, where f (t) =

Chapter 6, Problem 13

(choose chapter or problem)

Consider the initial value problem y__ + y = f (t), y(0) = 0, y_(0) = 0, where f (t) = u0(t) + 2 n _ k=1 (1)kuk (t). a. Draw the graph of f (t) on an interval such as 0 t 6 . b. Find the solution of the initial value problem. G c. Let n = 15. Plot the graph of the solution for 0 t 60. Describe the solution and explain why it behaves as it does. d. Investigate how the solution changes as n increases. What happens as n? 1

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