MATH 2065 Study Guide - Final Guide: Balts, Step Function, Partial Fraction Decomposition
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As usual, a copy of the table of laplace transforms from the text will be provided. In exercises 1 6, solve the given di erential equation. You are free to choose whatever technique that you deem to be most appropriate. y(1) = 2. y(0) = 2. y(0) = 1, y(cid:48)(0) = 3. 2 for t 5. (a) find f (s), the laplace transform of f (t). (b) find y (s), the laplace transform of y(t). (note: you may express your answer in terms of f (s). ) Do not solve for y(t): [14 points] find the laplace transform of each of the following functions. (a) f (t) = (t 3)2(h(t 2) h(t 4)) (b) g(t) = (t2 cos 2t)e 3t. Final exam: [14 points] compute each of the following inverse laplace transforms. (cid:189) (cid:189) (a) l 1 (b) l 1 (cid:190) s 10 s2 + s 2 e 2s s2 + 9 (cid:190) (cid:183) 1 1.
