hw_1_15_16_09

hw_1_15_16_09 - Ma 221 Homework Solutions Spring 2009 Due...

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Ma 221 Homework Solutions Spring 2009 Due January 15 / 16 , 2009 1.2 p.14 #1, 3, 5, 6, 7, 9, 8 1. (a) Show that x 2 x 3 is an explicit solution to x dy dx 3 y on the interval − , . Differentiating x gives: x 6 x 2 Substituting and for y and y : x dy dx 3 y xy 3 y x 6 x 2 3 2 x 3 6 x 2 6 x 2 This identity is true on − , and therefore x is an explicit solution on − , . (b) Show that x e x x is an explicit solution to dy dx y 2 e 2 x 1 2 x e x x 2 1 on the interval − , . Differentiating x gives: d dx d dx e x x e x 1 Substituting and for y and y : d dx x 2 e x 1 e x x 2 e x 1 e 2 x 2 xe x x 2 e 2 x 1 2 x e x x 2 1 e 2 x 1
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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_15_16_09 - Ma 221 Homework Solutions Spring 2009 Due...

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