ABSTRACT
If you have taken an elementary differential equations course, you are familiar with various techniques used to determine solutions of differential equations, as well as possibly some methods used to describe characteristics of the solutions corresponding to different initial conditions. Pushing beyond such a rudimentary analysis with an eye toward performing a more rigorous investigation inevitably requires some mathematical sophistication. Contrary to the opinion that mathematics is all about performing calculations to solve problems, discovery of patterns, forming cogent arguments, and performing careful analysis is at the heart of the discipline. But, how does one do mathematics carefully and properly?
