Change of Variable in a second-order PDE

Hello!

I am working on a question involving a P.D.E. in a adv. calc. course.

Consider the general homogenous second-order partial differential equation

with constant coefficients (a,b,c).

If , show that the substitution reduces the above equation to

So we must consider the change of variable from to , which is and take partial derivatives? I can't seem to derive the desired result, however, and I have double-checked my messy algebra...

Any help appreciated. Thanks!