ODE :: xy'' + y' +2xy = 0 :: Method of Frobenius Series Solution about a Regular Singular Point

In this video we apply the method of Frobenius to solve a differential equation xy'' + y' + 2xy = 0 with a power series expanded about the regular singular point x=0. We find a repeated indicial root, and a recurrence relation that has terms staggered by two. We also find that c1 = 0 making all odd coefficients, then, equal zero. Thus, the series solution we find here only has even exponents. ------------------ My name is Jonathan, and differential equations are one of the most useful and exciting applications of mathematics. I hope this video helps bring to light some of the techniques involved with the method of Frobenius for finding a power series solutions expanded about a regular singular point. Thanks for watching!