I've tried to solve the attached PDE, as is shown in the file.
As is stated in the file, it seems unreasonable that U1 explodes so I hope you'll find the error in what I did.
Thank you in advance
Is u(x,y) to satisfy that equation inside or outside the square? Typically solutions to Laplace's equation, given the value on some closed curve, have very different solutions inside and outside the curve.