The number of boundary conditions required to solve the differential equation $\frac{\partial^{2} ϕ}{\partial x^{2}} + \frac{\partial^{2} ϕ}{\partial y^{2}}$ is

2

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0

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4

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1

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Solution

The correct option is C $4$
The general solution of Laplace equation contains $4$ arabitrary constants. Therefore, we required $4$ boundary conditions.
i.e., $ϕ = (C_{1} c o s p x + C_{2} s i n p x) (C_{3} e^{p y} + C_{4} e^{- p y})$
where $C_{1}, C_{2}, C_{3}, C_{4}$ are arbitrary constatns.

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