How to solve this First Order Differential Equation?

[nontradstuden]

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'.

 

[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.

 

[nontradstuden]

Eh, I just found out what I did wrong. Simple mistake, but took hours to find it because I kept doing it... was dividing by N instead of M...

but Thank you for your assistance!