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.