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How to Solve dx/dt = Adx/dy + Bdx^2/dy^2

  1. Mar 14, 2009 #1
    Hello, I am trying to solve the following equation:

    [tex]\frac{\partial x}{\partial t} = A \frac{ \partial x}{\partial y} + B \frac{\partial^2 x}{\partial y^2}[/tex]

    I know how to solve the diffusion equation (i.e. no dx/dy term), but that method doesn't work here. I tried to go with the LaPlace Transform route, but I got an ugly term of the following form:

    [tex]\frac{-A-\sqrt{4 B s+A^2}}{2B} y [/tex]

    Which I can't find a handy inverse LaPlace for, and which Mathematica doesn't give a real answer to.

    Any suggestions how to approach this? Thanks.
  2. jcsd
  3. Mar 14, 2009 #2


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    Well, try with a separation of variables thingy, i.e:
  4. Mar 14, 2009 #3
    Thanks, that did the trick; nothing like forgetting day one of PDE class!
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