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-   -   How do one solve this PDE (http://www.physicsforums.com/showthread.php?t=580805)

 Inigma Feb23-12 10:08 PM

How do one solve this PDE

I have a battle with the following direct partial integration and separation of variables toffee:

I have to solve,
$u(x,y)=\sum_{n=1}^{∞}A_n sin\lambda x sinh \lambda (b-y)$

If there were no boundary or initial conditions given, do I assume that λ is $\frac{n\pi}{L}$ and do I then solve $A_n$? If I am going in the wrong direction here, please point me in the right direction... thanks!

 meldraft Feb24-12 06:31 AM

Re: How do one solve this PDE

As far as I know, there is no way to solve this further without boundary conditions. You need a condition of the type $u(x_0,y)=g(y)$ or $u(x,y_0)=g(x)$. By evaluating the equation with the boundary condition, you can use Fourier series to find the coefficient $A_n$.

 Inigma Feb24-12 08:15 AM

Re: How do one solve this PDE

Meldraft: