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Unformatted text preview: MATH 251 Final Exam December 20, 2007 Name: Student Number: Section: This exam has 15 questions for a total of 150 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. The point value for each question is in parentheses to the right of the question number. You may not use a calculator on this exam. Please turn off and put away your cell phone. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: Total: Do not write in this box. MATH 251 FINAL EXAM December 20, 2007 1. (6 points) What is the form of the general solution of the equation y ′′ y ′ 2 y = 4 t 2 e − t ? (a) y ( t ) = At 3 e − t + Bt 2 e − t + Cte − t (b) y ( t ) = t 2 ( A cos t + B sin t ) (c) y ( t ) = At 3 e − t + Bt 2 e − t + Cte − t + De − t + Ee 2 t (d) y ( t ) = t 2 e − t ( A cos t + B sin t ) 2. (6 points) Find the inverse Laplace transform of the function F ( s ) = 2( s 1) e − 2 s s 2 2 s + 2 . (a) 2 u ( t 1) e t cos t (b) 2 u ( t 2) e t − 2 cos( t 2) (c) 2 u ( t 2) e t − 2 sin( t 2) (d) 2 u ( t 2) e t sin t Page 2 of 11 MATH 251 FINAL EXAM December 20, 2007 3. (6 points) Which of the following initial value problems has more than one solution?...
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This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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