Chem Differential Eq HW Solutions Fall 2011 139

Chem differential eq hw solutions fall 2011 139

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Unformatted text preview: Section 8.1 The Laplace Transform 139 Also 2 (s − 3)(s + 2)(s2 − 2s + 2) = A CS + D B ++ + ; s−3 s + 2 (s − 3)(s + 2)(s2 − 2s + 2) 2 = A(s + 2)(s2 − 2s + 2) + B (s − 3)(s2 − 2s + 2) +(CS + D)(s − 3)(s + 2); s = −2 ⇒ B = −1/25 s = −3 ⇒ A = 2/25 constant term coefficient of s3 2 (s − 3)(s + 2)(s2 − 2s + 2) ⇒ 2= 6 8 + − 6D ⇒ D = −6/25; 25 25 ⇒ C = −1/25; = 2 1 −s − 6 − + 25(s − 3) 25(s + 2) 25(s2 − 2s + 2) = Y2 ; Now Y = −1 1 + + Y1 + Y2 5(s + 2) 5(s − 3) y = − 7 −2t 7 7 1 + e3t − et cos t + et sin t. e 50 25 50 50...
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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