# Thread: Finding the general soln. of a diff equ.

1. ## Finding the general soln. of a diff equ.

Hello Everybody!

can someone help me out with this question. I am struggling with it so much.

cos(x)* dy/dx + (sin(x)) * y = 1

Thanks a lot for your help, i appreciate it.

2. Originally Posted by kithy
Hello Everybody!

can someone help me out with this question. I am struggling with it so much.

cos(x)* dy/dx + (sin(x)) * y = 1

Thanks a lot for your help, i appreciate it.
Did you try $\displaystyle \text{Integrating factor}=e^{\int\sin(x)dx}$?

3. ## integrating factor

I don't know how to apply the integrating factor

4. Originally Posted by kithy
I don't know how to apply the integrating factor
Ok, here are two links to help you through this. If you have any problems just post back and someone here will be happy to help you

Integrating factor - Wikipedia, the free encyclopedia

Integrating Factor -- from Wolfram MathWorld

5. Originally Posted by kithy
Hello Everybody!

can someone help me out with this question. I am struggling with it so much.

cos(x)* dy/dx + (sin(x)) * y = 1

Thanks a lot for your help, i appreciate it.
Originally Posted by Mathstud28
Did you try $\displaystyle \text{Integrating factor}=e^{\int\sin(x)dx}$?
@Mathstud: Look at your own reference:
$\displaystyle cos(x)~\frac{dy}{dx} + sin(x)~y = 1$

$\displaystyle \frac{dy}{dx} + tan(x)~y = 1$

So the integrating factor is
$\displaystyle M(x) = e^{\int tan(x)~dx}$

-Dan

6. Originally Posted by topsquark
@Mathstud: Look at your own reference:
$\displaystyle cos(x)~\frac{dy}{dx} + sin(x)~y = 1$

$\displaystyle \frac{dy}{dx} + tan(x)~y = 1$

So the integrating factor is
$\displaystyle M(x) = e^{\int tan(x)~dx}$

-Dan
Dang it! I forgot to linearize it, . I am very very sorry Kithy if I caused some confusion.

7. Originally Posted by topsquark
@Mathstud: Look at your own reference:
$\displaystyle cos(x)~\frac{dy}{dx} + sin(x)~y = 1$

$\displaystyle \frac{dy}{dx} + tan(x)~y = 1$

So the integrating factor is
$\displaystyle M(x) = e^{\int tan(x)~dx}$

-Dan
Err..

$\displaystyle cos(x)~\frac{dy}{dx} + sin(x)~y = 1$

$\displaystyle \frac{dy}{dx} + tan(x)~y = \sec x$

Am I missing something?

8. I think that was just a typo.