I'm learning about the second order PDEs, and I've come across the transformation of variables I don't understand.

We have and a, b, c functions of class , which are not at the same time all equal to zero.

The equation in question is:

(*)

We introduce the change of variables:

,

How does the equation (*) now looks like?

I've tried googling change of variables, but I'm still lost.

Please, help.

Thank you.