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Unformatted text preview: MATH 251 FINAL EXAMINATION December 17, 2008 Name: Student Number: Section: This exam has 17 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. A list of Laplace transforms is attached as the last page of this booklet. It can be removed for easy reference during the examination. You may not use a calculator on this exam. Please turn off and put away your cell phone. 112: 13: 14: 15: 16: 17: Total: Do not write in this box. MATH 251 FINAL EXAMINATION December 17, 2008 1. (6 points) Suppose y ( t ) is the solution of the initial value problem y = 25 y 2 , y (6) = 1 . What is lim t →∞ y ( t )? (a) 5. (b) 5. (c) ∞ . (d)∞ . 2. (6 points) Consider all the nonzero solutions of the second order linear equation y 00 + 8 y + 16 y = 0 . As t → ∞ , they will (a) approach 0. (b) approach ∞ . (c) approach∞ . (d) some approach ∞ , while others approach∞ . Page 2 of 12 MATH 251 FINAL EXAMINATION December 17, 2008 3. (6 points) Let y 1 ( t ) and y 2 ( t ) be any two solutions of the second order linear equation t 2 y 00 6 ty + cos(3 t ) y = 0 . What is the general form of their Wronskian, W ( y 1 ,y 2 )( t )? (a) Ce 6 t (b) Ce 3 t 2 (c) Ct 6 (d) C t 6 4. (6 points) Consider the problems below. ( I ) y 00 4 y = 0 , y (0) = α, y (0) = β. ( II ) y 00 4 y = 0 , y (0) = α, y (10) = β. (a) Only ( I ) has a unique solution for every combination of real numbers α and β ....
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This note was uploaded on 07/16/2011 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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