- #1

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my work:

(1/F)(dF/dx)=(1/cosy)(cosy+siny)=1+tany

=>lny=x +xtany +c`

=> y =ce^(x+xtany)

however, the question wants the integrating factor to be e^x...

why?

- Thread starter asdf1
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- #1

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my work:

(1/F)(dF/dx)=(1/cosy)(cosy+siny)=1+tany

=>lny=x +xtany +c`

=> y =ce^(x+xtany)

however, the question wants the integrating factor to be e^x...

why?

- #2

HallsofIvy

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I don't know what you mean by "the question wants the integrating factor to be e^x"!

I wasn't aware that questions

- #3

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Isn't that equation seperable?

- #4

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you're right, it's "sinydx+ cosydy= 0"

that question wanted to prove that the integrating factor is e^x, but the integrating factor that i found was y =ce^(x+xtany)...

- #5

lurflurf

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[tex]\frac{\partial}{\partial y}u\sin(y)=\frac{\partial}{\partial x}u\cos(y)[/tex]

or

[tex]\frac{\partial u}{\partial y}\sin(y)+u\cos(y)=\frac{\partial u}{\partial x}\cos(y)[/tex]

integrating factors are not unique so assume

[tex]\frac{\partial u}{\partial y}=0[/tex]

- #6

HallsofIvy

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If the problem **says** "show that e^{x} is an integrating factor", thenyou don't have to **find** the integrating factor yourself (as lurflurf said, integrating factors are not unique), just multiply the equation by e^{x} and see if the result is exact.

If you got ce^(x+xtany) as an integrating factor, you sure like doing things the hard way! As I said earlier, 1/sin y is an obvious integrating factor (because, as Corneo said, the equation is separable. Multiplying by

1/sin y "separates" it)

If you got ce^(x+xtany) as an integrating factor, you sure like doing things the hard way! As I said earlier, 1/sin y is an obvious integrating factor (because, as Corneo said, the equation is separable. Multiplying by

1/sin y "separates" it)

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- #7

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lol...

i didn't think of that...

thank you very much!!! :)

i didn't think of that...

thank you very much!!! :)

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