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90 pts. Problem 1. In each part, find the general solution or solve the initial value problem. A. y 00 + y 0 − 6y = 0, y(0) = 7, y 0 (0) = −11. B. y 00 + 6y 0 + 9y = 0. C. y 00 + 6y 0 + 34y = 0. D. x2 y 00 + 5xy 0 + 4y = 0. 40 pts. Problem 2. Find the general solution. A. D2 (D − 2)3 (D − 1)y = 0 B. (D + 4)(D2 + 4D + 13)3 y = 0 60 pts. Problem 3. Use the method of Undetermined Coefficients (either version) to find the general solution A. y 00 − y 0 − 2y = x2 + 2 B. y 00 − y 0 − 2y = xex C. y 00 − 2y 0 + y = ex . 1 40 pts. Problem 4. Find the general solution by the method of variation of parameters. A. y 00 − 4y 0 + 4y = e2x x2 B. x2 y 00 + 2xy 0 − 6y = x3 You may assume the solution of the homogenous equation is y = C1 x2 + C2 /x3 . 2 EXAM Exam 2 Math 3350, Summer II, 2009 July 27, 2009 • Write all of your answers on separate sheets of paper. You can keep the exam questions when you leave. You may leave when finished. • You must show enough work to justify your answers. Unless otherwise instructed, give exact answers, not √ approximations (e.g., 2, not 1.414). • This exam has 4 problems. There are 230 points total. Good luck!