M251final(su10)

# M251final(su10) - MATH 251 Final Examination Name: August...

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MATH 251 Final Examination August 13, 2010 Name: Student Number: Section: This exam has 18 questions for a total of 150 points. In order to obtain full credit for partial credit problems, all work must be shown. For other problems, points might be deducted, at the sole discretion of the instructor, for an answer not supported by a reasonable amount of work. The point value for each question is in parentheses to the right of the question number. A table of Laplace transforms is attached as the last page of the exam. Please turn off and put away your cell phone. You may not use a calculator on this exam. Problem # Score Maximum 1–2: 12 points 3–4: 12 points 5–6: 12 points 7–8: 12 points 9–10: 12 points 11–12: 12 points 13: 6 points 14: 16 points 15: 16 points 16: 16 points 17: 12 points 18: 12 points Total: 150 points

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FINAL EXAMINATION August 13, 2010 Multiple Choice Section 1. (6 points) Consider the autonomous equation y 0 = y 2 ( y - 1)( y - 3) . Suppose y (10) = λ . Find all possible values of λ such that lim t + y ( t ) = 1. (a) -∞ < λ < 3 (b) -∞ < λ 1 (c) 0 < λ < 3 (d) 0 < λ < 2. (6 points) Let y 1 ( t ) and y 2 ( t ) be any two solutions of the second order linear equation t 2 y 00 - 3 ty 0 - t sin(4 t ) y = 0 . What is the general form of their Wronskian? (a)
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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 Penn State.

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M251final(su10) - MATH 251 Final Examination Name: August...

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