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m05x2f09 - Math 205 Second Exam N AM E Section(Last First...

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Math 205 Second Exam October 29, 2009 NAME : Section (Last, First) LECTURE : Prof. Skandera (MWF 9am, Sect. 10) Prof. Dodson (MWF 11am, Sect. 11) Prof. Dodson (MWF 3pm, Sect. 12) Prof. Zhang (TuTh 10:45 am, Sect. 13) Question 1: /20 Question 2: /20 Question 3: /15 Question 4: /25 Question 5: /20 Total: /100 Instructions : This is a 60 minute exam. You are not to have or use a calculator during the exam. You will be graded on the work shown on your paper; an answer without the correct supporting steps may receive no credit. Solutions to differential equations are not to include integrals; and must be expressed only in terms of real numbers and real functions.
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1. In this problem, solutions to differential equations are not to include integrals. (a) (10 points ) Solve the differential equation ( x 2 + 1) dy dx = xy and write your solution as an explicit function y = y ( x ) . (b) (10 points ) Solve the differential equation dy dx + 1 1 - x y = 1 - x, then solve the initial value problem y (0) = 1 .
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2. (20 points ) Find the general solution of the following differential equations. In
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