A diffusion problem is expressed by U/t = D(^2U/x^2) in which D is the diffusion coefficient. The initial condition and the boundary condition are U(x,0)=2cos((pi/2)*x) ;U(0,t)=2.0; and U(L,t) = 0; a). Convert the differential equation and the initial and boundary conditions to the dimensionless form with t*=tD/L^2 and x*=x/L (where L is the length). (15 points)