2065s10exf

2065s10exf - Name: Final Exam Instructions. Answer each of...

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Name: Final Exam Instructions. Answer each of the questions on your own paper. Put your name on each page of your paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. A table of Laplace transforms and the statement of the main partial fraction decomposition theorem have been appended to the exam. In Exercises 1 { 8, solve the given difierential equation. If initial values are given, solve the initial value problem. Otherwise, give the general solution. Some problems may be solvable by more than one technique. You are free to choose whatever technique that you deem to be most appropriate. 1. [ 12 Points ] 2 tyy 0 = 1 + y 2 , y (2) = 3. 2. [ 12 Points ] y 0 + 2 ty = t , y (0) = ¡ 3. 3. [ 10 Points ] y 00 + 10 y 0 + 29 y = 0. 4. [ 10 Points ] 4 y 00 + 12 y 0 + 9 y = 0. 5. [ 12 Points ] y 00 ¡ 4 y 0 + 3 y = 0 = 0, y (0) = 1, y 0 (0) = ¡ 1. 6. [ 12 Points ] y 00 + 2 y 0 ¡ 8 y = 4 e 2 t . 7. [ 10 Points ] 2 t 2 y 00 + 5 ty 0 ¡ 2 y = 0.
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2065s10exf - Name: Final Exam Instructions. Answer each of...

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