This is the electric potencial of a certain geometry; expoced in Example 3.5 in Griffiths, Introduction to Electrodynamics, 4th ed. This problem has a solution with the metod of partial diferencial ecuations called, separation of variables.
The animation is made in Wolfram Mathematica, you can download the code I made to animete this solution, here: Griffiths_Example_3.5