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Math Help - PDE solve

  1. #1
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    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.
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  2. #2
    Super Member Rebesques's Avatar
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    What about changing variables to the (suggested by the pde) z=x, w=f(y)...?
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