Question: For what values of $\displaystyle m $ and $\displaystyle n $ will $\displaystyle u = x^ny^m $ be an integrating factor for the differential equation

$\displaystyle (-3y-2x)dx + (5x+4x^2y^{-1})dy = 0 $

The exact differential equation which results from multiplying by this integrating factor has solution $\displaystyle F(x,y) = C $ where $\displaystyle F(x,y) =$___________________________.

Attempt at solving the question:

First I check to see whether either differential is exact (equal to each other), of course they are not.

The continue to solve and reach this point:

$\displaystyle u'(y)(-3y -2x) + u(y)(-3-2x) = u(y)(5+8xy^{-1}) $

$\displaystyle (-3y -2x)u'(y) + (-3-2x-5-8x^{-1}) = 0 $

$\displaystyle (-3y -2x)u'(y) + (-8-2x-8xy^{-1}) = 0 $

I should be able to factor something out, but i don't seem to find any, so am I doing the question wrong?