# HW3 - y(0 = 6 Problem 3 Find the solution of each of the...

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Assignment 3 Math 427K: Unique Number 58780 Due Wednesday, February 13, 2008 To obtain full credit, you must show all your work. Your assignments will not be accepted unless they are legible, neat, and stapled. Problem 1. Show whether or not each of the following is a general solution to the given ODE: a) y 00 - 3 y 0 + 2 y = 0 , c 1 e x + c 2 e 2 x b) y 00 - y 0 - 2 y = 0 , c 1 ( e - x + e 2 x ) c) y 00 - 3 y 0 + 2 y = 0 , c 1 ( e - x - e 2 x ) + c 2 e x Problem 2. Does the initial value problem have a unique solution? No solution? A non unique solution? When it makes sense, determine for each initial value prob- lem the largest open interval in which a solution is guaranteed to exist. Explain. a) y 00 + 2 y 0 + 3 y = 0 y (0) = 5 , y 0 (0) = 1 b) x 2 y 00 - y 0 - y = 0 , y ( - 1) = 2 , y 0 ( - 1) = 1 c) y 00 + xy 0 - y = 0 y (3) = y 0 (3) = 0 d) x 2 y 00 - y 0 - y = 0 , y (0) = 6
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Unformatted text preview: , y (0) = 6 Problem 3. Find the solution of each of the following equations and a (the) par-ticular solution satisfying the given conditions, if such conditions are given. a) y 00-y = 0 b) y 00-4 y-5 y = 0 , y (1) = 1 , y (1) = 0 , c) y 00-2 y-2 y = 0 , y (0) = 0 , y (0) =-5 d) y 00 + 5 y = 0 Problem 4. Solve problems 9, 11, 13, 27 and 28 from Chapter 3, Section 1 of the course textbook. Problem 5. Solve problems 8, 14 and 27 from Chapter 3, Section 2 of the course textbook. Problem 6. Solve problems 3, 12, 13, 15 and 22 from Chapter 3, Section 3 of the course textbook. 1...
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