M251final(sp00)

# M251final(sp00) - Name MATH 251 Final exam May 4 2000...

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MATH 251 Final exam May 4, 2000 Name: Section: There are 10 partial credit questions, each worth 15 points. In order to obtain full credit for these 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. You may not use a calculator on this exam. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: Total: Do not write in the box to the left

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MATH 251 -Final exam- 1. Solve the initial value problem y 0 = 2 t + 2 ty, y (0) = 3. Page 2 of 12
MATH 251 -Final exam- 2. Find the general solution to each of the following: (a) 4 y 00 - 4 y 0 + y = 0 (b) y 00 - 2 y 0 + 2 y = 0 (c) y 00 + 5 y 0 + 6 y = 0 Page 3 of 12

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MATH 251 -Final exam- 3. Find the form of a particular solution of the equation: y 00 + 4 y = t 2 e t - 2 cos 2 t + ( t + 1) sin t . DO NOT solve for the constants. Page 4 of 12
MATH 251 -Final exam- 4. (a) Find the Laplace transform of f ( t ) = ( 0 : 0 t < 3 t 2 : t 3 . (b) Find the inverse Laplace transform of s - 2 s 2 + 2 s + 10 .

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