Difficult differential equation

[Hydrolyziz]

Solve this differential equation:

xy'+y=x^2y^2

I've tried using the z subst. Nothing works so far. Any help would be great

 

[tiny-tim]

Welcome to PF!

Solve this differential equation:

xy'+y=x^2y^2

I've tried using the z subst. Nothing works so far. Any help would be great

Hi Hydrolyziz! Welcome to PF!

(have a squared: ² )

Divide by y² to give:

xy'/y² + 1/y = x² , and carry on from there.

(Hint: if the LHS was xy'/y² - 1/y, would you be able to integrate it?

divide by some function of x so that you can use a similar method )