I'm an undergrad student at a community college, and I am currently taking differential equations. My professor is offering people to hand in math papers for either extra credit or even complete test replacements. I am doing it because it just seems interesting despite me having a hard time with the class, but I don't have a single idea of going about it. My professor gave the example of Bernoulli's Equation and Riccati equation as topics for writing.
My problem is I don't know what to do, where to get started, or what to even write about. Do I just prove something and then talk about its applications?