So, I've worked out a few bugs with the program. Some times, it would spit out both the initial conditions and the results in (ye) such that my analysis was sometimes incorrect. I fixed some of the logic statements in the program and that cleared up the issue. Later, as I was testing a few other equations, I was getting problems that I hadn't seen before. The lines of code that were generating the error were in both my code and ode45. After tinkering with it for a bit, I changed the solver to ode113 and that seemed to clear up the issue.
I would like to note, however, that some of the equations will generate complex answers. It graphs according to the real part, and I do not think it does any analysis of the unreal part. I think this is what caused the problem with ode45. I will redo some of my analysis of earlier equations to ensure that my answers are consistent.
In the mean time, I've been conducting some background research to give me a better basis for both presenting the material and analyzing my results. Specifically, I need to explain how these equations arise naturally, what the initial conditions mean, and what my data indicates. For this reason, I started looking at the Quantum Optics book.