# M251ex1(sp04) - Name: MATH 251 Midterm Exam I Feb. 26, 2004...

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MATH 251 Midterm Exam I Feb. 26, 2004 Name: Student Number: Instructor: Section: This exam has 10 questions for a total of 100 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. THE USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINATION. At the end of the examination, the booklet will be collected. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: Total: Do not write in this box.

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MATH 251 Spring 2004 Exam I 1. (5 points) Consider the initial value problem: dy dt = 1 y - 3 t 2 , y ( t 0 ) = y 0 Give conditions on the values of t 0 and y 0 so that you are guaranteed to Fnd a unique solution to the problem. Do not attempt to solve the equation for y ( t ). Page 2 of 10
MATH 251 Spring 2004 Exam I 2. (12 points) For the autonomous equation y 0 = y 3 + 2 y 2 - 3 y a)Find all equilibrium solutions. b) Determine the stability of each equilibrium solution you found in part (a). Justify your conclusions. c) Let

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## This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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M251ex1(sp04) - Name: MATH 251 Midterm Exam I Feb. 26, 2004...

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