Test3_sol

Test3_sol - MAC 2312-01,02,03 Calculus II Test 3 Dr Jungmin...

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MAC 2312-01,02,03 Calculus II Test 3 October 31, 2008 Dr. Jungmin Choi Name Instructions. 1. This test has 7 pages including this page. There are 6 problems. 2. Show all your work. You may not receive any credit from a correct answer, if there is no relevant work leading to the answer. 3. Do not separate the pages of the test. If any pages do become separated, write your name on them and point them out to your instructor when you turn in your test. 4. You are not allowed to use a calculator. 5. Please turn oF all cell phones and pagers and remove all headphones. Problem Points Score 1 15 2 10 3 20 4 20 5 20 6 15 Total 100 You may need the following formula. sin 2 θ = 1 - cos 2 θ 2 cos 2 θ = 1 + cos 2 θ 2 1
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1. (a) Solve the differential equation. (5 points) dy dx = x e y ± e y dy = ± xdx e y = 1 2 x 2 + C y =ln | 1 2 x 2 + C | . (b) Find the solution of the differential equation that satis±es the given initial condition. (10 points) dy dx = x 2 y 2 ,y (0) = 0 ± y 2 dy = ± x 2 dx 1 3 y 3 = 1 3 x 3 + C After using the initial condition y (0) = 0 , we have y 3 = x 3 or y = x.
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This note was uploaded on 03/14/2011 for the course MAC 2312 taught by Professor Zhang during the Fall '07 term at FSU.

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Test3_sol - MAC 2312-01,02,03 Calculus II Test 3 Dr Jungmin...

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