hw_1_27_09

# hw_1_27_09 - MA 221 Homework Solutions Due date Tuesday pg...

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MA 221 Homework Solutions Due date : Tuesday , January 27 , 2009 pg . 65 Sec . 2 . 4 # 9 ̄ , 11 , 13 , 1 ̄ 5 ̄ , 17 , 1 ̄ 9 ̄ , 23 , 25 , 27a , 29 (Underlined Problems are not turned in) In problems 9, 11, 13, 15, 17 and 19, determine whether the equation is exact. If it is, then solve it. 9 ̄ .) 2 xy 3 dx x 2 1 dy 0 Computing partial derivatives we obtain: M y y 2 xy 3 2 x N dx x x 2 1 2 x M y N x the equation is exact. Integration yields: F x , y M x , y dx 2 xy 3 dx x 2 y 3 x f y F y x 2 f y x 2 1 f y 1 f y 1 dy y C general solution is F x , y x 2 y 3 x y C or explicitly, y C 3 x x 2 1 11.) cos x cos y 2 x dx sin x sin y 2 y dy 0 Computing partial derivatives we obtain: M y y cos x cos y 2 x cos x sin y , N dx x sin x sin y 2 y  cos x sin y M y N x the equation is exact. Integration yields:

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## This note was uploaded on 09/22/2009 for the course MA MA221 taught by Professor Levine during the Spring '09 term at Stevens.

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hw_1_27_09 - MA 221 Homework Solutions Due date Tuesday pg...

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