# How do one solve this PDE

1. Feb 23, 2012

### Inigma

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!

2. Feb 24, 2012

### meldraft

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 $A_n$.

3. Feb 24, 2012

Meldraft: