(a) Find the general solution of by solving the eigenvalues and the corresponding eigenvectors. (10%)

3.Find the steady-state temperature T(x,y) in the thin rectangle plate 0≦xs≦ 10, 0≦y≦20 by solving the Laplace equation. The upper side of the rectangle is kept at u(x) ℃, the lower side is kept at 0℃, and the other two sides are perfectly insulated. Perfectly insulated means no temperature change across the boundary. (20%)