Uxx means second derivative with respect to x
Uyy means second derivative with respect to y
Uxx + Uyy = 0, 0 < x < pi, 0 < y < 1
Ux(0,y) = 0 = U(pi,y), 0 < y < 1
U(x,0) = 1, U(x,1) = 0, 0 < x < pi
Please show all work including how eigenvalues and eigenvectors are derived.
This shows how to solve a problem regarding a wave equation.