This is sort of a homework question but I'm not looking for an answer. I'm just trying to understand exactly what's going on. It says "Among all the equations of the form [the general second order linear homogeneous partial differential equation], show that the only ones that are unchanged under all rotations (rotationally invariant) havce the form a(uxx + uyy) + bu =0. What exactly does it mean for an equation to be rotated? I don't understand what's going on here very well.