MATH 256 Midterm: MATH 256 2013 Winter Test 1
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One 8. 5 11 sheet of notes, written or printed on both sides, is allowed. No books or calculators or other notes are allowed. [20] 1. (a) verify that y1(t) = et is a solution of the homogeneous equation y t t 1 y + 1 t 1 y = (t 1)et, t > 1. (2) 4 3 (cid:21) x. (a) find the general solution if a > 1. (b) find the general solution if a = 1. [20] 3. (a) find the laplace transform of. 1 t < 2, t 2. (b) use the de nition of the laplace transform l{f (t)} = r properties of the -function (or unit impulse function) to show that. 0 e stf (t) dt, integration by parts, and. L{ (t c)} = se cs, if c > 0. (c) solve the initial value problem y + 4y = g(t) 1. 2 , y (0) = 0, where g(t) is as given in part (a).
