Proving a property of homogeneous equation that is exact The following question was given to us in an exam:
If $0=M dx + N dy$ is an exact equation, in addition to the fact that $\frac{M}{N} = f\Big(\frac{y}{x}\Big)$ is homogeneous, then 
$xM_x + yM_y = (xN_x + yN_y)f$.
Now I had absolutely no idea how to prove this question. I tried doing $M = Nf$ and taking derivatives and multiplying by $x$ or $y$, and you get the required R.H.S. but with the extra term $N(\frac{-f_x}{x} + \frac{f_y}{x})$ added. How does one approach a question like that??
I  have never encountered a question like that, not even when solving for different types of integrating factors to get an exact equation or when working with a homogeneous equation.
Anyone got any ideas? Please don't post a complete solution.
Thanks.

So the solution should be:
As $\frac{M}{N} = f\Big(\frac{y}{x}\Big)$, this means that the degree of homogeneity of $M$ and $N$ must be equal.
So $xM_x + yM_y = aM$, and $xN_x + yN_y = aN$, by euler's homogeneity theorem where $a$ is the degree of homogeneity of $M$ and $N$. 
So dividing the first by the second of these equations, and one should get 
$xM_x + yM_y = \frac{M}{N} (xN_x + yN_y) = f\Big(\frac{y}{x}\Big)(xN_x + yN_y )$.
Is that correct?
