Consider the initial value problem y + y = fk(t), y(0) = 0, y (0) = 0, where fk(t) =
Chapter 6, Problem 16(choose chapter or problem)
Consider the initial value problem y + y = fk(t), y(0) = 0, y (0) = 0, where fk(t) = [u4k(t) u4+k(t)]/2k with 0 < k 1. (a) Find the solution y = (t, k) of the initial value problem. (b) Calculate limk0 (t, k) from the solution found in part (a). (c) Observe that limk0 fk(t) = (t 4). Find the solution 0(t) of the given initial value problem with fk(t) replaced by (t 4). Is it true that 0(t) = lim k0 (t, k)? (d) Plot (t, 1/2), (t, 1/4), and 0(t) on the same axes. Describe the relation between (t, k) and 0(t).
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