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For the PDE

$$ u_{xx}+u_{yy} + c^2u = 0$$

We have $$ \frac{X''}{X} + \frac{\ddot{Y}}{Y} + c^2 = 0$$

How in general should we determine the separation constant, $\lambda$? And in this case what would be the most suitable one?

Btzzzz
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1 Answers1

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$$\begin{cases}\frac{X''}{X}=\lambda\\\frac{Y''}{Y}=-\lambda-c^2\end{cases}$$ Or, if you prefer $$\begin{cases}\frac{X''}{X}=\lambda'-\frac{c^2}{2}\\\frac{Y''}{Y}=-\lambda'-\frac{c^2}{2}\end{cases}$$ or other expressions since you can chose any $\lambda$ as you like.

JJacquelin
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