integrating factor proof/ partial derivative wrt xy

The full question is:

show that if where R depends only on xy, then the differential equation M+N*y'=0 has an integrating factor of the form U(xy). Find a general formula for this integrating factor.

Using an equation from the text for U (for which finding a solution, U, means that the differential equation above is exact) I have:

then substituting in

and equating coefficients of N and M respectively,

and

**Is there some way that I can find the derivative of U wrt xy using the partial derivatives of U wrt x and y that I have above? Then I could integrate wrt xy to find U, right?**