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LCSphysicist

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**Homework Statement::**All below

**Relevant Equations::**,

Generally, when for example we need to solve ##\nabla u = 0##, we separate variables and find equations like that ##X''/X = -Y''/Y = k^2##. So we just solve it, sum the solutions and make it satisfy the boundary/initial conditions.

But, sometimes we also need to consider the case when ##k=0##, that is, we need to consider solutions of the type ##x, y, xy, const.##.

While it becomes apparent the necessity of these terms when we are solving the problem, i would like to know if there is a way to realize right at the beginning if we would need to consider these other solutions.

For example, ##u = 0## at ##x=0, y = 0, x = L; u = 30## at ##y = H## does not need it. But ##u_y = 0## at ## x=0, x=L; u = 0## at ##y=0; u = f(x)## at ## y = H## need it.

How could i know right at the beginning? Of course this is just one example, i would like to know for any general case, even for differents differential equations other than ##\nabla u = 0##

**[Moderator's note: moved from a homework forum.]**

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