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The differential equation is:
(1.1)
With the boundary conditions:
(1.2)
And:
(1.3)
We start by writing the function as a product of two independent functions:
(1.4)
Then, the partial differentials turn into full differentials:
(1.5)
(1.6)
The boundary conditions now become:
(1.7)

Plugging (1.5) and (1.6) back into (1.1) we get:

(1.8)
Equation (1.9) is separated. Each side of the equation is completely independent of the other side. Since it must be true for any , the two sides must be equal the same constant:
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Solution Summary

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