Change of Variable in a second-order PDE
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!