Unlike the intended solution, nearly all correct solutions submitted in the first two weeks have employed advanced mathematical techniques beyond the IPhO syllabus. Here is a hint to help you avoid the need for such advanced techniques.
The electrostatic potential inside a homogeneously charged ellipsoid is a quadratic polynomial of the coordinates (see https://physicscup.ee/solution-of-problem-1-pc-2024/ and scroll down to the figure with ellipsoids).
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com.