Consider the initial value problem y + 2ay + (a2 + 1)y = 0, y(0) = 1, y (0) = 0. (a)
Chapter 3, Problem 26(choose chapter or problem)
Consider the initial value problem y + 2ay + (a2 + 1)y = 0, y(0) = 1, y (0) = 0. (a) Find the solution y(t) of this problem. (b) For a = 1 find the smallest T such that |y(t)| < 0.1 for t > T. (c) Repeat part (b) for a = 1/4, 1/2, and 2. (d) Using the results of parts (b) and (c), plot T versus a and describe the relation between T and a.
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