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M251final(sp10)

# M251final(sp10) - MATH 251 Name Final Examination May 3...

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MATH 251 Final Examination May 3, 2010 FORM A Name: Student Number: Section: This exam has 16 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. 1 thru 11: 12: 13: 14: 15: 16: Total: Do not write in this box.

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MATH 251 FINAL EXAMINATION May 3, 2010 1. (6 points) Consider the autonomous equation y 0 = 4 y 2 - y 4 . Suppose y (99) = λ and lim t →∞ y ( t ) = 2, ﬁnd all possible value(s) of λ . (a) - 2 < λ < (b) λ = 2 (c) 0 < λ < (d) 0 < λ < 2 2. (6 points) Consider the two problems below. ( I ) y 00 + λy = 0 , y (0) = 2 π, y 0 (0) = β. ( II ) y 00 + λy = 0 , y 0 (0) = 0 , y 0 (2 π ) = β. (a) Only ( I ) has a unique solution for every combination of real numbers λ and β . (b) Only ( II ) has a unique solution for every combination of real numbers λ and β . (c) Each has a unique solution for every combination of real numbers λ and β . (d) Neither is guaranteed to have a unique solution for every combination of real numbers λ and β . Page 2 of 12
MATH 251 FINAL EXAMINATION May 3, 2010 3. (6 points) Let y 1 ( t ) and y 2 ( t ) be any two solutions of the second order linear equation ty 00 + 4 y 0 - t 2 e - 6 t y = 0 . What is the general form of their Wronskian, W ( y 1 ,y 2 )( t )? (a)

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M251final(sp10) - MATH 251 Name Final Examination May 3...

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