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Unformatted text preview: Math 20D, Final Exam Solutions December 4, 2006 Name: Section: This exam consists of 12 pages including this front page. The last page is the table of Laplace transforms. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use two 4by6 index cards, both sides. 4. You have two hours for this exam. Score 1 10 2 10 3 10 4 10 5 10 6 10 7 15 8 10 9 5 10 10 Total 100 1 1. (a) Find the general solution of y 00 + 5 y = 0 . The characteristic equation is r 2 + 5 = 0, which gives r = ± i √ 5. Thus the general solution is y = C 1 cos √ 5 t + C 2 sin √ 5 t. (b) Find the general solution of dy dt = y t . dy y = dy t ln  y  = ln  t  + C  y  = e ln  t  + C  y  = e c e ln  t   y  = e c  t  y = ± e c t. Therefore y = Ct. 2 2. Solve the following initial value problem. y y = 2 te 2 t , y (0) = 1 This is first order linear. The integrating factor is μ = e t . So ( e t y ) = 2 te t e t y = 2 te t 2 e t + C y = 2 te 2 t 2 e 2 t + Ce t ....
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This note was uploaded on 06/12/2008 for the course MATH 20D taught by Professor Mohanty during the Spring '06 term at UCSD.
 Spring '06
 Mohanty
 Math

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