Practice exam 2-427K - x = 0 , y 00 + xy + 2 y = 0 , y (0)...

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Math 427K Practice Exam 2, Fall 2011 1. (15 pts)Find the general solution of y (4) - 16 y =0 . 2. For the DE 2 x 2 y 00 +3 xy 0 +(2 x 2 - 1) y =0 , ( x> 0) (a) (10 pts) Show that x = 0 is a regular singular point. (b) (10 pts) Find the roots of the indicial equation F ( r )= r ( r - 1) + p 0 r + q 0 (c) (10 pts) Find the ±rst three terms of the series solution corresponding to the larger root. 3. (25 pts) Find the series solution of the initial value problem when
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Unformatted text preview: x = 0 , y 00 + xy + 2 y = 0 , y (0) = 0 , y (0) = 2 and compute the rst 3 nonzero terms of this series. 4. (a)(15pts) Find the general solution of the system x 1 = x 1-2 x 2 , x 2 = 3 x 1-4 x 2 . (b)(15pts) Plot a few trajactories of the system and describe the behavior of the solution as t ! 1 . 1...
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