I am familiar with the usual heat equation, however, my lecturer gave me this problem and it does not look like anything I have ever seen (in my whole entire life and I am not just being dramatic).
$\frac {\partial T}{\partial t} =\frac {1}{r^2} \frac{\partial}{\partial r} ( r^2 \frac {\partial^2 T}{\partial r^2} + \frac2r\frac {\partial T}{\partial r})$
Okay, I realized that I cannot possibly expand it out because it will be very messy and it will contain a third order equation (and also someone told me not to expand it out). I was thinking of substitution however I have not found a suitable substitute that I can work here. Any ideas?