Given the following PDE
$$x^{2} \frac{\partial^{2} u}{\partial x^{2}} = \frac{\partial u}{\partial t}$$
how could one reduce it to the heat equation? I've been trying to substitute either the function or just the variable $x$, but nothing that I try seems to work.
I'm more interested in the method one could use to reduce it to the heat equation rather than just being given the exact substitution. Any help is much appreciated.