For a real function $f(x, y)$ with $x=x(t)$ and $y=y(t)$ state the chain rule for the derivative $\frac{d}{d t} f(x(t), y(t))$.

By changing variables to $u$ and $v$, where $u=\alpha(x) y$ and $v=y / x$ with a suitable function $\alpha(x)$ to be determined, find the general solution of the equation

$$x \frac{\partial f}{\partial x}-2 y \frac{\partial f}{\partial y}=6 f$$