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Unformatted text preview: Department of Mathematics Final Exam Math 39100 Spring 2006 Part I (71pts) Answer all problems. 1. (8pts) Find the general solution to y + 2 ty = 2 te t 2 . 2. (9pts) Find the solution to y = (1- 4 x ) y 2 , y (0) =- 1 2 . 3. (8pts) Find the general solution to 2 y 2 + sin x + (4 xy + cos y ) dy dx = 0 . 4. (a) (5pts)Find the general solution to the differential equation: y 00- 2 y- 3 y = 0 (b) (7pts) Use part a) to help find the general solution to y 00- 2 y- 3 y = 3 sin t. 5. (8pts) Find all solutions to the differential equation: 2 x 2 y 00 + 3 xy + 4 y = 0 , x > . 6. (9pts) Find an approximation of the general power series solution, around x = 0, for the differential equation: y 00 + 2 xy + y = 0 , by giving the first five terms of the series solution (the series solution through the x 4 term). 7. (8pts) Use separation of variables to replace the partial differential equation: tu xx + xu t = 0 , where u is a function of x and t with two ordinary differential equations. Do NOT solve the...
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- Spring '11