Exam 2 Review - MATH 3321 Sample Questions for Exam 2...

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MATH 3321 Sample Questions for Exam 2 Linear Nonhomogeneous Differential Equations 1. Find the general solution of y ±± - 4 x y ± + 6 x 2 y = 4 x 2 . 2. Find the general solution of y ±± +4 y =2tan2 x . 3. Find the general solution of y ±± - 6 y ± +9 y =4 e 3 x + e 3 x x . 4. Find the general solution of y ±± y =4cos2 x . 5. Find the general solution of y ±± y =2s in2 x . 6. Find the general solution of y ±± - 6 y ± +8 y =2 e 4 x +6. 7. A particular solution of the nonhomogeneous differential equation y ±± - 2 y ± - 15 y =2cos3 x +5 e 5 x +2 will have the form: 8. A particular solution of the nonhomogeneous differential equation y ±± - 8 y ± +16 y = e 2 x sin 4 x e 4 x x will have the form: Laplace Transformations 1. Find the Laplace transform of f ( x )=2 e - 3 x + cos 2 x x . 2. Find the Laplace transform of f ( x )=3 xe βx + e x sin 3 x . 3. If F ( s )= 2 s 2 + s - 3 s 2 , then L - 1 [ F ( s )] is: 4. If F ( s 1 ( s - 3) 2 + s s 2 - 4 s +13 , then L - 1 [ F ( s )] is: 5. Find the Laplace transform of the solution of the initial-value problem y ± y =3cos2 x ; y (0) = 3 .
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This note was uploaded on 02/09/2011 for the course MATH 3321 taught by Professor Morgan during the Fall '08 term at University of Houston.

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Exam 2 Review - MATH 3321 Sample Questions for Exam 2...

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