M251final(fa00)

# M251final(fa00) - MATH 251 Final exam Dec 15 2000 Name...

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MATH 251 Final exam Dec. 15, 2000 Name: Student Number: Instructor: Section: There are 9 partial credit questions. 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 USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINA- TION. At the end of the examination, the booklet will be collected. 1: 2: 3: 4: 5: 6: 7: 8: 9: Total: Do not write in the box to the left

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MATH 251 -Final exam- 1. (16 pts) Solve the initial value problem y 0 - 2 y = t 2 e 2 t , y (0) = - 1 . Page 2 of 10
MATH 251 -Final exam- 2. (16 pts) Find the general solution to each of the following: (a) y 00 + 4 y 0 + 5 y = 0 (b) y 00 - 6 y 0 + 9 y = 0 (c) y 00 + y 0 - 20 y = 0 Page 3 of 10

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MATH 251 -Final exam- 3. (16 pts) Find the form of a particular solution of the equation: y 00 + 9 y = 7 sin 3 t + 2 te t - t 2 . D O NOT solve for the constants! Page 4 of 10
MATH 251 -Final exam- 4. (16 pts) Solve the following initial value problem: y 00 + 4 y = δ ( t - π ) , y (0) = 0 , y 0 (0) = 3 . Page 5 of 10

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MATH 251 -Final exam- 5. (18 pts) Let A = - 3 4 2 4 .
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