- #1

- 734

- 0

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?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter asdf1
- Start date

- #1

- 734

- 0

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

Science Advisor

Homework Helper

- 41,847

- 967

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

- 321

- 0

Isn't that equation seperable?

- #4

- 734

- 0

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

Homework Helper

- 2,440

- 138

[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

Science Advisor

Homework Helper

- 41,847

- 967

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)

Last edited by a moderator:

- #7

- 734

- 0

lol...

i didn't think of that...

thank you very much!!! :)

i didn't think of that...

thank you very much!!! :)

Share: