Thread: PDE solve

This is a question from past exam paper. I am preparing for exams in June and am stuck. Can anyone please help ?

Show that the PDE:

Uxx + [2/F’(y)]Uxy + [1/F’ (y)2]Uyy = 0

is parabolic.
Find and solve for its characteristic coordinate. F' (y) here is differentiable and its indefinite integral is monotonic.
Find also a suitable non-characteristic coordinate and hence write the PDE in its canonical form.
I have done the first 2 parts but completely stuck on the last. Any help please ?
Thanks in advance.

What about changing variables to the (suggested by the pde) z=x, w=f(y)...?