I have a square area with the length a. The temperature surrounding the square is T_0 except at the top where it's T_0(1+sin(pi*x/a)). They ask for the stationary temperature in the area. In other words, how can the temperature u(x,y) inside the area be written when the time = infinity.(adsbygoogle = window.adsbygoogle || []).push({});

The first thing I do is that I realize that u(x,y) can be written u(x,y) = sum(X(x)*Y(y)).

I also think that it should be a nice starting point to create v = u-T_0, that gives me that the surrounding temperature is 0 everywhere except at the top where it's T_0*sin(pi*x/a)

experience tell me that X(x) = sin(k*pi*x/a)

But how do I find Y(y)? cant seem to get it right.

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# Determ the stationary temp with a PDE

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