This paper will provide several results for the reducibility of second order differential operators. More specifically, we will discuss second order operators that factor into two first order operators with either; one constant coefficient and one rational function coefficient, two polynomial coefficients, or two rational function coefficients with regular singularities. Furthermore, we will only consider operators with one or two regular singularities when considering rational function coefficients. The discussion will provide tests for reducibility of the operators as well.

Author Bio

Results from the paper have been presented in a lecture at the Arkansas-Oklahoma Regional MAA Conference and in an undergraduate poster competition at the Joint National Meeting in New Orleans. This fall, I will attend the University of Nebraska-Lincoln as a graduate teaching assistant in pursuit of a doctorate in mathematics. Right now, I am entertaining the idea of concentrating in analysis or differential equations within graduate school. In my spare time, I enjoy reading and being active in some form of physical exercise. I also love to volunteer in the community and church for various youth programs.