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M251ex1(sp05) - Math 251 First Exam NAME Section There are...

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Math 251 February 24, 2005 First Exam NAME: Section #: There are 9 questions on this exam. Question 9 is worth 12 points. Each other question is worth 11 points. The points assigned to each part of the question are indicated at the start of the part. Show all your work . Partial credit may be given. The use of calculators, books, or notes is not permitted on this exam. Please turn off your cell phone before starting this exam. Time limit 1 hour and 15 minutes. Question Score 1 2 3 4 5 6 7 8 9 Total
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1. a. 9pts Find the general solution to the following ODE ty + 2 y = 2 t > 0 b. 2pts Find the solution of the above equation which satisfies y (1) = 0.
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2. a. 3pts Verify that the following ODE is exact: 2 t + e y + ( te y - cos y ) dy dt = 0 (Show your work.) b. 6pts Find the general solution to the ODE in Part a. (You may leave your answer in implicit form.) c. 2pts Find the solution to the ODE in Part a. which satisfies y (1) = π/ 2. (You may leave your answer in implicit form.)
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3. 11pts Solve the following ODE.
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