Suppose you have an equation: M(x,y) dx + N(x,y) dy = 0 I have heard that there always exists an integrating factor u(x,y) such that the partial derivative of uM with respect to y equals the partial derivative of uN with respect to x. But somewhere in the back of my mind I remember that there is a condition that the guarantee of the existence of the integrating factor is valid ONLY if there are no singularities in the region. Can someone please tell me the exact status regarding singularities is? Thank you very much. I appreciate it a lot.