5. (a) Find the power series solutions y = E=o Cnx" of the differential equation (DE) (x – 1)y" + 5y = 0 about the ordinary point x = 0. What is the interval of convergence of your power series...

Extracted text: 5. (a) Find the power series solutions y = E=o Cnx" of the differential equation (DE) (x – 1)y" + 5y = 0 about the ordinary point x = 0. What is the interval of convergence of your power series solution? (b) Find the singular point(s) and classify the singular point(s) of the DE 2xy" + 5y' + xy = 0, and use the method of Frobenius to obtain series solutions of the DE about the singular point(s).