test_2 - h ( t ) = te t . (You don’t have to check this.)...

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MA 341-001 Test 2 S. Schecter March 24, 2006 Use your own paper to work the problems. On all problems, you must show your work to receive credit. When you fnish, Fold this paper lengthwise together with your work, so that this writing is on the outside. Write your name and row number above (the Front row is row 1), and turn in. 1. Determine the Form you would use For a particular solution in the method oF undeter- mined coe±cients. Do not solve For the coe±cients. (a) y ′′ + 4 y = te 2 t (b) y ′′ + 4 y = 6 sin 2 t 2. ²ind the general solution using the method oF undetermined coe±cients. y ′′ + 3 y + 2 y = 8 t 2 - 30 3. Use the variation oF parameters to fnd a particular solution. y ′′ - 2 y + y = t 4 e t ²or this problem, the impulse response Function is
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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 ( t-s ) 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) e-6 s ( s +4) 3 2...
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This test prep was uploaded on 03/31/2008 for the course MA 341 taught by Professor Schecter during the Spring '08 term at N.C. State.

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test_2 - h ( t ) = te t . (You don’t have to check this.)...

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