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Nov 21, 2021 at 14:58 comment added akhmeteli @physicsguest : Then it seems V(x,y)=20x-10 is the solution you need.
Nov 21, 2021 at 14:47 comment added physicsguest Well that's what I'm trying to find. I'm finding the coefficients (A, B, C, D) to the solution of laplace's equation; nabla^2V = 0 in order to get the complete solution. I am trying to do this by matching the boundary conditions to the equation V(x,y) I have written above. It's literally electrostatics. There is an electric potential applied at each boundary of the square and you are trying to find V(x, y) inside of it.
Nov 21, 2021 at 5:34 history answered akhmeteli CC BY-SA 4.0