Hello, I am trying to solve the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums - The Fusion of Science and Community**