(b) y" + 6y'+ 10y = 30* cos2t,y(0) = 0,y'(0)= 2. The "*"means convolution.(12%)

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%)