I have an equation of the form

$\displaystyle x\frac{{\delta q}}{{\delta y}} + y\frac{{\delta q}}{{\delta x}} = 0$.

How would I go about showing that $\displaystyle q = f\left( {x/y} \right)$ is a solution? Can I say that $\displaystyle \frac{{\delta q}}{{\delta y}} = \frac{{ - x}}{{{y^2}}}$, and continue like that? I'm a bit confused with the fact that it's $\displaystyle q = f\left( {x/y} \right)$ and not just $\displaystyle q = x/y$.

Any help appreciated!