# Integrating Factor of $(axy^2+by)dx+(bx^2y+ax)dy=0$. [duplicate]

This question already has an answer here:

$$(axy^2+by)dx+(bx^2y+ax)dy=0$$

I have asked this question before too, but i wish to know the method for evaluating the integrating factor which is $\dfrac {1} {(a-b)(x^2y^2-xy)}.$

So far i know:

$M(x,y)dx + N(x,y)dy=0$ is said to be a perfect differential when

$\frac{\partial (M(x,y))}{\partial y}=\frac{\partial (N(x,y))}{\partial x}$.

In this case the equation is not exact and integrating factor is multiplied to make the differential equation exact.

Is there any other method to solve this differential equation?

## marked as duplicate by Empty, user147263, mrf, rogerl, Michael GaluzaAug 31 '15 at 5:31

• i have this integrating factor $${\frac {1}{x \left( xy \left( x \right) -1 \right) y \left( x \right) }}$$ – Dr. Sonnhard Graubner Aug 30 '15 at 14:45