Help me with my diffeque homework
Solve the equation xy" + y' + xy = 0 by means of a power series about the point x0 = 0. more 5.2: 2, 5, 7(a) Find eigenvalues and eigenfunctions of the boundary value problem: y" - lamda y = 0, y(0) = 0. more 10.1: 14-16 Determine the equilibrium points and classify each one as asymptotically stable, unstable, or semistable. Draw the plase line and sketch several typical graphs of solutions in the ty-plane, dy/dt = y2( 1 - y2) more 2.5: 7-13 Find the Fourier series for the function: f(x) = f(x + 4) = f(x). And sketch the graph of the function to which the series converges for three periods, more 10.2: 13-23 Solve the boundary value problem by the method of separation of variables: alpha2uxx = ut, 0 0, u(0, t) = 0, u(L, t) = 0, t > 0 more 10.5: 1-5; 7, 8.