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Math 1220 Quiz 11 Due: December 1 Answer the questions below. The value of each question is indicated at the beginning of it. Please indicate which convergence test you are applying in each case. Name: UID: 1. Use a power series expansion to show that the differential equation y 00 (x) + y(x) = 0, has solution y(x) = cos x. y(0) = 1, y 0 (0) = 0 2. In quiz 6 you showed that the differential equation y 00 (x) + 4y 0 (x) + 5y(x) = 10ex , y(0) = 1, y 0 (0) = 2 has solution y(x) = ex + e−2x sin x (i) Find a power series expansion in x of the function f (x) = ex + e−2x sin x through terms of order 3. (ii) Find the power series expansion of the solution to the differential equation y 00 (x) + 4y 0 (x) + 5y(x) = 10ex , y(0) = 1, y 0 (0) = 2 through terms of order 3. You should recover the series in part (i). Page 2