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Unformatted text preview: MATH 251 Examination II November 8, 2010 FORM A Name: Student Number: Section: This exam has 12 questions for a total of 100 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 6: 7: 8: 9: 10: 11: 12: Total: Do not write in this box. MATH 251 EXAMINATION II November 8, 2010 1. (5 points) Consider the nonhomogeneous second order linear equation y 00 + 25 y = 3 e 5 t- 2 t sin5 t. Which function below is the most suitable choice of the form of particular solution Y that you would use to solve the given equation using the Method of Undetermined Coefficients? (a) Y = Ae 5 t + ( Bt + C ) cos5 t + ( Dt + E ) sin5 t (b) Y = Ate 5 t + ( Bt + C ) cos5 t + ( Dt + E ) sin5 t (c) Y = Ae 5 t + ( Bt 2 + Ct ) cos5 t + ( Dt 2 + Et ) sin5 t (d) Y = Ate 5 t + ( Bt 2 + Ct ) cos5 t + ( Dt 2 + Et ) sin5 t 2. (5 points) Consider the fourth order linear equation y (4) + 9 y 00 = 0 . What is its general solution? (a) y ( t ) = C 1 e t + C 2 e- t + C 3 cos3 t + C 4 sin3 t (b) y ( t ) = C 1 cos √ 3 t + C 2 sin √ 3 t + C 3 t cos √ 3 t + C 4 t sin √ 3 t (c) y ( t ) = C 1 cos t + C...
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