- #1

tommyhakinen

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## Homework Statement

[tex]\frac{\partial^{2}u}{\partial t^{2}} = a^{2} \frac{\partial^{2}u}{\partial x^{2}}[/tex] (x>0, t>0)

with u(0,t) = t, u(x,0) = 0, u

_{t}(x,0) = A.

Solve the PDE using laplace transform.

## The Attempt at a Solution

I have managed to get the transform:

[tex]\frac{\partial^{2}U(x,s)}{\partial x^{2}} - \frac{s^{2}}{a^{2}}U(x,s) = - \frac{A}{a^{2}}[/tex]

How should I continue from here? How do I find the solution for U(x,s)? If using Integrating factor, how should I do it? thanks..

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