Chapter 12, Problem 20RE

If the four edges of the rectangular plate in Problem 19 are simply supported, then show that the given particular solution satisfies the boundary conditions

w(0, y) = 0, w(a, y) = 0, 0 < y < b

w(x, 0) = 0, w(x, b) = 0, 0 < x < a

${\frac{{\partial }^{2}w}{\partial x^2}|}_{x=0}=0$, ${\frac{{\partial }^{2}w}{\partial x^2}|}_{x=a}=0$, 0 < y < b

${\frac{{\partial }^{2}w}{\partial y^2}|}_{y=0}=0$, ${\frac{{\partial }^{2}w}{\partial y^2}|}_{y=b}=0$, 0 < x < a.