# Homework Help: How to solve this First Order Differential Equation?

1. Sep 27, 2011

How to solve this differential equation?

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

I've tried finding an integrating factor in order to make it exact, but I don't know what to do with this.

The answer is given as x^(3)y^(2) + xy^(3) = c

I'm so confused.

I separated it and found My and Nx. I've also tried finding an integrating factor, but it isn't a function of 'xy'.

Last edited: Sep 27, 2011
2. Sep 27, 2011

### LCKurtz

Presumably you have written it in the form

(3x2y+y2)dx + (2x3+3xy)dy = 0

You are correct that it is not exact. But it may have an integrating factor that is a function of x or y only which will make it exact. Look at

http://www.sosmath.com/diffeq/first/intfactor/intfactor.html

I think you will find one of those two tests works.

3. Sep 27, 2011