Department of Mathematics and Computer Science
Master of Science
In this thesis, the reader will be made aware of methods for finding power series solutions to ordinary differential equations. In the case that a solution to a differential equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since many differential equations which yield such a solution model an actual physical situation. In this thesis, we introduce conditions that guarantee existence and uniqueness of analytic solutions, both in the linear and nonlinear case. Several methods for obtaining analytic solutions are introduced as well. For the sake of pure mathematics, and particularly in the applications involving these differential equations, it is useful to find a radius of convergence for a power series solution. For these reasons, several methods for finding a radius of convergence are given. We will prove all results in this thesis.
Lagrange, John, "Power Series Solutions to Ordinary Differential Equations" (2001). Masters Theses & Specialist Projects. Paper 672.