Solving dy/dx = (y² + xy²)/(x²y - x)

[dec46]

Hi All,

I am a postgrad student looking for help in solving this ODE.

Homework Statement

$$\frac{dy}{dx}$$=$$\frac{y^{2}+xy^{2}}{x^{2}y-x}$$

Homework Equations

The Attempt at a Solution

I have been attempting to solve this by substitution but without success, any help would be appreciated.

 

[tjackson3]

It looks separable.

 

[dec46]

The furthest I can get is

$$x(xy-1)dy=(x+1)y^{2}dx$$

but do not know where to go from here?