M251final(fa10)

M251final(fa10) - MATH 251 Final Examination December 15,...

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Unformatted text preview: MATH 251 Final Examination December 15, 2010 FORM A 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. 1 thru 14: 15: 16: 17: 18: Total: Do not write in this box. MATH 251 FINAL EXAMINATION December 15, 2010 1. (6 points) Find the solution of the initial value problem y = cos t sin y , y (0) = 2 . (a) y = cos- 1 (- sin t ) (b) y = cos- 1 (sin t- 1) (c) y =- sin- 1 (cos t ) (d) y = sin- 1 (- cos t + 2 ) 2. (6 points) Which initial or boundary value problem below is guaranteed to have a unique solution according to the Existence and Uniqueness theorems? (a) y 00 + sin(5 t ) y- cos(10 t ) y = , y (0) = 1 , y (0) =- 1 . (b) ( t + 2) y- e- t y = t, y (- 2) = 0 . (c) y 00 + 100 y = 0 , y (0) = 9 , y (2 ) =- 10 . (d) t 2 y 00 + ty + y = 0 , y (0) =- 2 , y (0) = 3 . Page 2 of 12 MATH 251 FINAL EXAMINATION December 15, 2010 3. (6 points) Let y 1 ( t ) and y 2 ( t ) be any two solutions of the second order linear equation 2 ty 00 + 4 y- t 3 cot(2 t ) y = 0 . What is the general form of their Wronskian, W ( y 1 ,y 2 )( t )? (a) Ct 4 (b) Ce- 4 t (c) Ce 2 t (d) Ct- 2 4. (6 points) Which of the functions below is a particular solution of the nonhomogeneous linear equation y 00 + 3 y + 2 y = 2 t + 1?...
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M251final(fa10) - MATH 251 Final Examination December 15,...

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