MATH 256 Midterm: MATH 256 2008 Winter Test 2
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Linear di erential equations. (a) solve the initial value problem: y + 3y = 2e 2t, y(0) = 1. (b) solve the initial value problem: y + 2ty = e t. Find the general solution of the following homogeneous linear system: x = 1. 3! x, and sketch the phase plane close to x = 0. Page 5 of 11 pages (b) find the solution of the following initial value problem: x = 1. The function f (t) is de ned for t [ 1, 1] by f (t) =( t 1, , 1 t, t [0, 1], t [0, 1], (a) sketch the function f (t) over the interval t [ 1, 1], and nd the fourier series for f (t). Page 7 of 11 pages (c) find the general solution of: y + 2y = f (t), (d) where f (t) is the function in part (a), assuming is a positive constant satisfying < .
