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Exam 2 Review

# 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 = 2 tan 2 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 + 9 y = 4 cos 2 x . 5. Find the general solution of y + 4 y = 2 sin 2 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 = 2 cos 3 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 + 2 e 4 x + 5 x will have the form: Laplace Transformations 1. Find the Laplace transform of f ( x ) = 2 e - 3 x + cos 2 x + 5 x . 2. Find the Laplace transform of f ( x ) = 3 x e βx + e x sin 3 x . 3. If F ( s ) = 2 s 2 + s - 3 s 2 + 4 , then L - 1 [ F ( s )] is: 4. If F ( s ) = 1 ( s - 3) 2 + s + 2 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 + 2 y = 3 cos 2 x ; y (0) = 3 .

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