MATH 211 Midterm: MATH 211 NIU Exam3Solution
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You must show your work and justify your answers to receive credit. Clearly indicate your answers by circling them: (15 pts. ) Determine the solution y(x) of the initial value problem y = y2e3x, y(0) = 1: (15 pts. ) Find the solution y(x) of the initial value problem (x 1)y + 2y = (x 1), y(2) = 1. Page 2 of 8: (14 pts. each) find the general solution of each of the following di erential equations. (a) 4xy1/2 + x2 2x 1/2y1/2 + (cid:16)2y + x2y 1/2 2x1/2y 1/2(cid:17) dy dx. Use the method of undetermined coe cients to nd the general solution y(x) of y(4) + 2y 8y = x2: (14 pts. ) Use the variation of parameters method to nd the general solution y(x) of cos 2x y + 4y = Use laplace transforms to nd the solution x(t) of the initial value problem x + 2x + 5x = et, x(0) = 0, x (0) = 1.
