Hi, could you please help me solve these.

(1) Make a substitution to linearise the Ricatti equation f' + 2f2 = Axc, where A is a constant. Hence solve the equation. (2) Find the general solution of the equation x?y" - 3xy' + 3y = 2x* cos x. You may use the fact that y(x) = x is a solution of the homo- geneous problem for extra credit. (3) Solve the equation (1 - 22)y" - 2xy' + 20y = 0 by means of a power series expansion. (4) Use the method of Frobenius to solve the equation x?y" + 2xy' + (x+ 3)y = 0. The Gamma function will help here. Express the solution in terms of Bessel functions. (5) Let y1, ..., yn be linearly independent solutions of the linear ODE an ( 2 ) y (7 ) + . .. + ao(x ) y = 0, xEICR. Show that y1, ..., Un cannot be simultaneously equal to zero. That is, there does not exist a E I such that y1(a) = . . . yn(a) = 0