ODE:: y'' - xy' + 2y=0 :: Power Series Solution about an Ordinary Point

Here, we derive two linearly independent solutions of a differential equation y''-xy'+2y=0 using a power series expansion about an ordinary point. An ordinary point is one that is not singular. A singular point is one that make the coefficient of y'' zero. As there are no singular points in this example we see every point is ordinary. This is the standard approach to finding solutions about ordinary points. --------------- My name is Jonathan, and I have taught thousands of students. Solving a differential equation is exciting to me every single time. The thrill of the problem is unique for each one, and I hope to provide useful strategies and techniques for using power series to solve differential equations for you to implement.