Suppose ux y solves the Laplaces equation on the unit square

Suppose u(x, y) solves the Laplace\'s equation on the unit square (x, y) [0, 1] time [0, 1] with boundary conditions: u_x(0, y) = u_y(x, 0) = u_y(x, 0) = 0. Select the only boundary condition for the right side of the square that is consistent with solutions of Laplace\'s equation. Justify your answer. u_x(1,y) = sin(pi y) u_x(1,y) = sin(2 pi y) u(1,y) = sin(pi y) u(1,y) = sin(2 pi y)

Solution

boundary condition for consistant u(1 ,y) = sin(2piy)

because laplace equation described on unit square [0,1] x [0,1]