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poisson equation

I am trying to solve poisson equation:

diff(diff(u(y,z),y),y)  + diff(diff(u(y,z),z),z) = 1

using separation of variables method.

The boundary conditions for the problem are:


can you please guide me to a good reference which will help me in
solving this problem using separation of variables.

Do you know how to solve this equation using mathematica

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