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

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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 finish, 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 coefficients. Do not solve for the coefficients. (a) y ′′ + 4 y = te 2 t (b) y ′′ + 4 y = 6 sin 2 t 2. Find the general solution using the method of undetermined coefficients. y ′′ + 3 y + 2 y = 8 t 2 - 30 3. Use the variation of parameters to find a particular solution. y ′′ - 2 y + y = t 4 e t For 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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