I need to find all the separated solns of(adsbygoogle = window.adsbygoogle || []).push({});

[tex] x^2 \frac{\partial^2 u}{\partial x^2} + x\frac{\partial u}{\partial x} + \frac{\partial^2 u}{\partial y^2} = 0 [/tex]

in the strip [tex]{(x,y) : 0 < y < a, -\infty < x < \infty } [/tex]

the separated solns must also satisfy u = 0 on both the edges, that is, on y=0 and y=a for all values of x.

Iv got the general solutions to be..

[tex] X(x) = Dlnx + C , (k = 0) [/tex]

[tex]X(x) = Dx^{n} + Cx^{-n} , (k \neq 0) [/tex]

and

[tex]Y(y) = A\cos{ky} + B\sin{ky} , (k \neq 0)[/tex]

[tex]Y(y) = Ay + B , (k = 0)[/tex]

where k is just the constant iv let the two bits equal when I separated the variables. (well -k^2 actually).

I just need help interpreting the conditions to sort out the constants..I think!

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# Applying Initial Conditions

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