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Unformatted text preview: h ( t ) = te t . (You don’t have to check this.) Recall that the variation oF parameters Formula says that a particular solution oF my ′′ + by ′ + ky = f ( t ) is given by y p ( t ) = i t h ( ts ) f ( s ) ds. 1 4. Find Y ( s ), the Laplace transform of the solution y ( t ) of the following initial value problem. Do not simplify Y ( s ), and do not ±nd y ( t ). y ′′ + 6 y ′ + 9 y = t 3 e − 5 t y (0) = 2 , y ′ (0) =3 5. Find the inverse Laplace transform of the following functions. (a) 10 − 2 s s 2 +2 s +10 (b) s 2 − 4 s ( s − 1) 2 (c) e6 s ( s +4) 3 2...
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 Spring '08
 Schecter
 Differential Equations, Equations, Laplace, impulse response function, following initial value

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