I have the following equation

$\displaystyle \frac{\partial}{\partial y}\left(y\frac{dm}{dx}+m\frac{dy}{dx}\right)-\frac{dm}{dx}=0$

where $\displaystyle m$ is a function of $\displaystyle y$ (say $\displaystyle m=f\left(y\right)$) and $\displaystyle y$ is a function of $\displaystyle x$ (say $\displaystyle y=g\left(x\right)$). Are there any conditions under which $\displaystyle \frac{dm}{dx}$ becomes identically zero and hence this equation can be reduced to the follwoing form which is easier to solve:

$\displaystyle \frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0$

If such condtions do not exist, what is the best and easiest method to solve the original equation?