MAT514-2006Spring

MAT514-2006Spring - MAT 514, Spring 2006 Introduction to...

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Unformatted text preview: MAT 514, Spring 2006 Introduction to Ordinary Differential Equations Final Exam Friday, May 5 You have 120 minutes to work the following 7 problems (10 pages). Correct answers without complete steps will not give full credit. Show ALL your work. Write all your solutions in clear, logical steps. Good luck! Your Name: Problem 1. (lOp.) Solve the initial value problem ty' + 2y - 4t 2 = 0, y(l) = 2 and describe the behavior of the solution as t ---+ 00. Problem 2. (3+7+5=15p.) (a) Show that the differential equation (2x - y) dx + (2y - x) dy == 0 is exact. (b) Solve the initial value problem (2x - y) dx + (2y - x) dy == 0, y(l) = 3. (c) Determine the interval in which the solution is valid. Problem 3. (lOp.) Find the solution of the initial value problem v" + 5y' + 6y = 0, y(O) = 2, y'(O) = 3 and describe the behavior of the solutions as t increases. Problem 4. (S+lO==lSp.) (a) Find the general solution of the differential equation y" + 4y == O. == O....
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MAT514-2006Spring - MAT 514, Spring 2006 Introduction to...

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