MTHE 225 Quiz: quiz 4 (10).pdf
20 Nov 2012
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1. (a) using only the de nition of the laplace transform, nd the laplace transform of f (t) where. 0 t 3 t > 3. 0 f (t)e st dt f (t)e st dt +z e2te st dt +z . F (s) is unde ned at s = 2, due to the vanishing denominator. However, from the de nition of the laplace transform, f (t)e 2t dt e2te 2t dt +z . = 3: find a particular solution of the equation y + y + 1. Based on f (x) = 1 + e x/2, our rst attempt at yp might be yp = a + be x/2. But we should check for any duplication with the homogeneous solution yc. The characteristic equation is r2 + r + 1. 2)2 = 0 which has a double root r = 1.
