(a) Let y be a function of t. Use Laplace transforms to solve the initial value problem * - 6 + 9y = tet, v(0) = 0, = 6 at t = 0. (15 marks) %3D %3D (b) Find the inverse Laplace transform of F(s) 3D (5 marks) s2 + 6s + 11 (c) Find the general solution of the equation -2y 4- x. (20 marks) (a) Use the substitution y = zx, where z is a function of r, to solve the differential equation x =y(x +y), r> 0. (15 marks)