In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.
Helmholtz Differential Equation--Bipolar Coordinates
See also
Laplace's Equation--Bipolar CoordinatesExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Helmholtz Differential Equation--Bipolar Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HelmholtzDifferentialEquationBipolarCoordinates.html