Thread: First Order Question

If i have:

(3y^2+2xy)dx-(2xy+x^2)dy=0

I firstly tried to solve this with Exact equations method. The partials I found were not equal therefore i assumed an integrating factor as a function of x and y. For both i did not come up with anything, as I got the factors as functions of both and x and y.

Then I proceeded to use the Homogenous Substituion v= y/x.
This lead me to getting a solution 2y+x=C.

I'm not sure if my approach is correct. I know for homogenous whenever the form y/x is recognizable, we proceed with this approach. But when is it correct to use the Exact Equations method?

Thanks.

you are in right direction .

then DE
reduce to

resolve into partial fraction