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partial differential equation help watch

1. Is the general solution to this equation:

This?
Where A and B are constants of integration.

If so how would I go about doing this question:
Determine the u(x,y) which satisfies the boundary condition;
2. anyone?
3. No. The y exponent should be twice the x exponent.

You can also combine AB into one constant since they are both constant.

It might help to superpose solutions, i.e.

4. I actually have no idea what to do. The sin y is confusing me. Do I have have to use or somehing else?
5. (Original post by flipper_99)
I actually have no idea what to do. The sin y is confusing me. Do I have have to use or somehing else?
Let

Fix so that if you set x = 1, the sum becomes the expansion of siny.
Hint:
Spoiler:
Show
it would be useful to set A_0 = 1 + 1 to get the required first term for the siny expansion
6. Do you mean ?

Even so, I still have no idea. Do you mean the taylor expansion for sine? I bet it's something trivial, but I just can't seem to see it. Quite annoying
7. (Original post by flipper_99)
Do you mean ?

Even so, I still have no idea. Do you mean the taylor expansion for sine? I bet it's something trivial, but I just can't seem to see it. Quite annoying
yeah, sorry. I've edited the previous post to the correct form.

See http://en.wikipedia.org/wiki/Sine#Series_definitions

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Updated: November 13, 2008
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