For u(x,y) defined on the square domain of 0

For u(x,y) defined on the square domain of 0 x 1 and 0 S y 1, solve the PDE D 2 u 02 u DX2 Dy2 with the boundary conditions, (i) u(0,y)=0 (ii) u(l,y) = sin(TtVY) (iii) u(x, 0) = 0 (iv) u(x, 1) = 4 (x 3 x 6) Make a contour plot of the solution, u(x, y). See Additional Note in the last page for an example of using Matlab to make a contour plot. The recommended contour interval for the plot is 0.05. For this problem, we expect the solution to be expressed as an infinite series. Please see the remark below HW 1 -QI on how to truncate the series and numerically compute the expansion coefficients.