I need help understanding how to solve this Laplace equation

Last updated: 5/12/2023

I need help understanding how to solve this Laplace equation The method that I tried is by using a perturbation but I got stuck trying to get the values of the perturbation at u 0 and u theta to be the same value 2 20 1 1 U 0 1 U 0 2 AU sine u 4 0 0 u r U 1 0 0 U 2 0 g 0