midrev3 - y 00 + 9 y = 10 e 2 t , y (0) =-1 , y (0) = 5 ....

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MAP 2302 Fall 2010 Review for Midterm 3 Format: 5 problems, 20 points each. Time allowed: 50 minutes. Laplace Transforms: properties of L.T., computing direct and inverse L.T., solving initial value problems with L.T., L.T. of discontinuous and periodic functions, solving systems of differential equa- tions with L.T. In problems (1–3), determine the Laplace transform: f ( t ) = e 2 t - t 3 + t 4 - e t sin t (1) f ( t ) = ± e - t , 0 t 1 , t, t > 1 . (2) f ( t ) = t 2 u ( t - 2) (3) In problems (4–6), determine the inverse Laplace transform: F ( s ) = s 2 + 16 s + 9 ( s + 1)( s 2 + s - 6) (4) F ( s ) = 1 s 4 - 1 (5) F ( s ) = e - 3 s (4 s + 2) ( s - 2)( s - 3) (6) In problems (7–8), use the Laplace transform to solve the given equation/system:
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Unformatted text preview: y 00 + 9 y = 10 e 2 t , y (0) =-1 , y (0) = 5 . (7) x 00 + y = 1 , x (0) = 1 , x (0) = 1 , x + y 00 = 1 , y (0) = 1 , y (0) =-1 . (8) y 00-5 y + 6 y = e t , y (0) = y (0) = 1 . (9) In problems (1011), nd the Laplace transform of the given function (assume that t 0): f ( t ) = | sin t | . (10) g ( t ) = t, < t < 1 , 1-t, 1 < t < 2 , (11) and g ( t ) has period T = 2....
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