# 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

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.