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I have the following Poission problem in 2D,

$-\Delta T(x,y) = f$ where $f = 8x$

I understand how to use separation of variables by assuming the solution is on the form $T(x,y) = X(x)Y(y)$ in the homogenous case where $f=0$ however I'm a bit confused when we've got $f=8x$.

I haven't found any clear examples, any help or guidance would be greatly appreciated.

SGM
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  • Hint: $T(x,y)=4xy^2$ is a solution to the inhomogeneous equation. – Jake28 Dec 30 '20 at 12:28
  • Thanks! So, adding $T(x,y) = 4xy^2$ to the solution obtained when solving the homogenous problem with corresponding BC's yields the general solution? – SGM Dec 31 '20 at 14:34

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