An Excursion into Differential Equations

This paper will be exploring the theory of differential equations through a specific example. We will build up the theorems to guarantee a solution. Then we will explore a power series solution. With the power series solution we are able to notice some similarities to a famous type of differential equation. We will then build up the theory behind these equations know as Bessel functions and finally be able to write our solution in terms of them. We will also explore generalizations of our equations and see if we can say anything about how their solutions may look.