I'm trying to come up with some sort of solution to the following differential equation--I warn you, it is ugly. Any help would be much appreciated.
$$D=(1-z)z^2\partial^2_z-[z^2-2\frac{zw(1-z)}{z-w}]\partial_z+(1-w)w^2\partial^2_w-[w^2-2\frac{zw(1-w)}{w-z}]\partial_w$$
$$D^{*}=\frac{zw}{w-z}[(1-z)\partial_z-(1-w)\partial_w]$$
$G_4, E_4, E^{*}$ are all known functions with various parameters.
The differential equation is: $$DG^{*}+D^{*}G_4=G_4E^{*}+G^{*}E_4$$
Are there any techniques that lend themselves well to this type of equation?
Thanks!
