test1_spring_04

# test1_spring_04 - Name Answers MA-366 Spring 2004 Test 1...

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MA-366, Spring 2004, Test 1 Name: Answers Note: You may use scratch paper. If the space provided is not enough, continue on the back or attach additional sheets (well organized). Show your work. Calculators are not allowed. Problem 1. (12 points) Solve the initial value problem x dy dx C 2y D e ± x ,y ( ± 1) D 3. and determine the largest interval where the solution is deﬁned. Answer: This is a linear equation. The general solution is y(x) D C ± (x C 1)e ± x x 2 . The solution of the IVP is D 3 ± (x C 1)e ± x x 2 , deﬁned for t < 0 . 1

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MA-366, Spring 2004, Test 1 2 Problem 2. (12 points) Solve the initial value problem (1 ± e x ) dy dx D y C ye x ,y ( ln 2) D 4, and determine the largest interval, where the solution is deﬁned. Answer: This is a separable equation. The solution is y(x) D 2e x (1 ± e x ) 2 , x > 0 .
MA-366, Spring 2004, Test 1 3 Problem 3. (12 points) Solve the initial value problem y 2 dy dx D 1 C y 2 , y(0) D 1. Answer: Separable equation. Implicit solution: y ± arctan (y) D x C 1 ± ± 4 .

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MA-366, Spring 2004, Test 1 4 Problem 4. (12 points)
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test1_spring_04 - Name Answers MA-366 Spring 2004 Test 1...

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