Answer Happy

Here is the solution, need help getting there, the more
explanation the better, Thanks!!
14) (10.5) Use separation of variables to find product solutions of the partial differential equation, 𐐀u Ju == + u. əx ду
14) For = -λ X' Y'+Y X Y X(x) = c₁e-2x, Y(y) = c₂e-(2+1)y u(x, y) = c₂e-((x+y)+y)