I am not very sure if this is a proper question, but I'm trying to investigate what the area of math can offer in researching the differential equation in polar coordinates: $r'^2+r^2=(kt)^2$, ...
Differential operators preserving the space of harmonic functions (aka higher symmetries of the Laplacian)
The article http://arxiv.org/abs/hep-th/0206233 (published in Ann. of Math. (2) 161 (2005), no. 3) deals with linear differential operators $D$ for which there exists another linear differential ...