Homework 3 solutions

Homework 3 solutions - AMS 361: Applied Calculus IV (DE...

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Unformatted text preview: AMS 361: Applied Calculus IV (DE & BVP) Homework 3 Assignment Date: Sunday (02/18/2009) Collection Date: Wednesday (03/04/2009) Quiz-1 on 2/25/2009 Grade: Each problem is worth 10 points (Problem 3.1, Prob. 25, P. 71) Find the general solutions of the following differential / equation. Primes denote the derivatives with respect to x: Solution: 1 , √ . Substitute , √ , √ ρ x , : √ Therefore, 2 , 3 √1 √ 3√1 , ,4 : (Problem 3.2, Prob. 28, P. 71) Find the general solutions of the following differential equation. Primes denote the derivatives with respect to x: Solution: , 2 x 2 , ρ x 2 2 , : , : ln Therefore, (Problem 3.3, Prob. 47, P. 72) Find the general solutions of the following second-order differential equation: (Hint: Introduce substitution / .) Solution: , 1 v , : ln| Therefore, , ln| |, | , : (Problem 3.4, Prob. 49, P.72) Find the general solutions of the following second-order differential equation: Solution: , 0, 1 1 1 1 1 1 0 0 , , = , √ 6 (Problem 3.5, Prob. 22, P.76) Solve equation: Solution: Substitute 6 x / 12 2 x 12 , . 4 2 , x 4 ρ x 4 4 2 / 2 2 , C=constant (Problem 3.6, Prob. 25, P.76) Solve equation: Solution: 2 x 3, 1 2 x 1 , 3 1 ρ x 1 1 3 3 , 1 1 1 1 , C=constant ...
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This note was uploaded on 05/11/2009 for the course AMS 361 taught by Professor Staff during the Spring '08 term at SUNY Stony Brook.

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