Q1/ What is the relationship between Laplace transform L[u(t)] = F(s) = est u(t)dt 0 and the following transform 00 -st [u(t)] = W(s, v) = e evu(t)dt Q2/ Use Adomian decomposition method to solve the following nonlinear partial differential equations: uxx + u² - u² = 0, with initial conditions u(0,y) = 0, ux(0, y) = cos(y). Q3/ Use DJM to solve the following nonlinear Schrodinger equation: iut +uxx+2lulu = 0, u(x, 0) = ex Q4/Use SAM to solve the following differential equation: a²u(x, y) u(x, y) + u(x,y) = 0, дх² ay² with initial conditions u(o, y) =y, ux (0,y) = y + coshy. ====artomain==== Q5/ Use Laplace homotopy perturbation method to solve the following nonlinear partial differential equation: a²u(x, y, t) at² a² = (uxx Uyy). дхду дхду (xy ux uy) - u, with the initial conditions u(x, y, 0) = ey, u(x, y, 0) = exy.