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- Feb 10th 2010, 02:10 AM #1

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## Need help with PDE problem

Could anyone help me with this? The question is under the spoiler tag.

__Spoiler__:

The PDE equation is separable, but the boundary conditions are non-homogeneous and are in partial derivatives.

I can answer if the equations are all homogeneous or if the boundary conditions are not homogeneous and not derivatives. But I'm not quite sure how to proceed with this one.

I would appreciate any help.

- Feb 10th 2010, 04:50 AM #2

- Feb 10th 2010, 05:31 AM #3

- Feb 10th 2010, 07:12 AM #4

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A function that is equal to -1 at x= 0 and 0 at x= l is . Integrating that, a function whose derivative is -1 at x= 0 and 0 at x= l is .

If you let , then .

That is, you now have the differential equation

with boundary conditions

and initial condition

With those boundary conditions, you can write v as a Fourier cosine series:

.

- Feb 10th 2010, 08:40 PM #5

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- Feb 11th 2010, 06:49 AM #6