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

  • Thread starter Peregrine
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  • #1
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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.
 

Answers and Replies

  • #2
arildno
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Well, try with a separation of variables thingy, i.e:
[tex]x(y,t)=F(y)*G(t)[/tex]
 
  • #3
22
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Thanks, that did the trick; nothing like forgetting day one of PDE class!
 

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