Why Is This First Order Non Linear Differential Equation So Challenging?

[Darkestsolrac]

Homework Statement

(8x^2y^3-2y^4)dx+(5x^3y^2-8xy^3)dy=0

Homework Equations

The Attempt at a Solution

I've already tried the most logical steps. The equation isn't exact and I couldn't find an integrating factor to make it exact. It's also not homogeneous or separable. I have to be making an error somewhere. I've done all my other questions but this one is just killing me. Help please!

 

[Simon Bridge]

(8x^2y^3-2y^4)dx+(5x^3y^2-8xy^3)dy=0
...
I've already tried the most logical steps.

Did you get rid of the common factor of y^2 :$$\frac{dy}{dx}=\frac{2y^2-8x^2y}{5x^3-8xy}$$
... where does this come from?