5. Consider Laguerre's equation xy" + (1 − x)y' + Ay = 0 where X is a constant. This ODE arises from Schödenger's equation in quantum mechanics (solutions describe the radial behaviour of the electron's wave function in the hydrogen atom). (a) Show that x = 0 is a regular singular point. (b) Show that the roots of the indiical equation are equal and write down the first few terms of the Froebenius series solution (i.e. the one not involving logarithms). (c) When Am, where m is a positive integer, show that the solution you obtained reduces to a polynomial (i.e. it truncates).