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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 Galuza Aug 31 '15 at 5:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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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 '15 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. $\endgroup$ – yasir Aug 31 '15 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. $\endgroup$ – yasir Aug 31 '15 at 23:48