Consider Laplace’s equation inside a rectangle 0 ≤ x ≤ L, 0 ≤ y ≤ H, with the boundary c...

Consider Laplace’s equation inside a rectangle 0 ≤ x ≤ L, 0 ≤ y ≤ H, with the boundary conditions

(a) What is the solvability condition and its physical interpretation?

(b) Show that u(x, y) = A(x² − y²) is a solution if f(x) and g(y) are constants [under the conditions of part (a)].

(c) Under the conditions of part (a), solve the general case [non constant f(x) and g(y)]. [Hints: Use part (b) and the fact that f(x) = fav + [f(x) − fav], where