Q. solve 4xyz=pq+2p*square(x)*y+2qx*square(y),using partial differential equations.
I think we will need a bit more information. At the moment all I can suggest
is that you assume p and q are functions of x, y and z and take partial
derivatives with respect to these variables in some order to reduce this to
a PDE, but quite what one would do with it from there I'm not sure.
Best to probably try that and see what you get.
RonL