# Math Help - Messy Differential Equation!?

1. ## Messy Differential Equation!?

I have this differential equation:

$(y-x) dy/dy=2(y^2-dy/dx)$

2. Originally Posted by Yehia
I have this differential equation:

$(y-x) {\color{red}dy/dy}=2(y^2-dy/dx)$

The red one is $\,\ \frac{dy}{dx}$ ?

3. Originally Posted by Ted
The red one is $\,\ \frac{dy}{dx}$ ?

YES it is! sorry my bad, it is dy/dx. youre right. can you help?

4. Isolate the derivative and then put it into differential form:

$(y-x)y'=2y^2-2y'$

$y'(y-x+2)=2y^2$

$dy(y-x+2)=2y^2 dx$

Now, can you find an integrating factor?

5. Originally Posted by shawsend
Isolate the derivative and then put it into differential form:

$(y-x)y'=2y^2-2y'$

$y'(y-x+2)=2y^2$

$dy(y-x+2)=2y^2 dx$

Now, can you find an integrating factor?

I follow you till there. But whats an integrating factor? and how can you move the x's to the dx's and the y's to the dy's???? please help further! thank!!