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

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?

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    $\begingroup$ i have this integrating factor $${\frac {1}{x \left( xy \left( x \right) -1 \right) y \left( x \right) }} $$ $\endgroup$
    – Dr. Sonnhard Graubner
    Aug 30, 2015 at 14:45
  • $\begingroup$ i don't understand why people are marking this as "duplicate" when i have already written in quotes that i have asked these question before too. $\endgroup$
    – miyagi_do
    Aug 31, 2015 at 10:06
  • $\begingroup$ It's simple common sense that if someone asking it again it is a different question else he is a paranoid and i can assure you i am not one of them. And i was to link it with my previous question but it was too late. You people have closed it. $\endgroup$
    – miyagi_do
    Aug 31, 2015 at 23:48

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