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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?

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Have you asked about this to your professor? –  Lord Soth Feb 25 '14 at 1:56
You should be askign all this to your professor. How can we possibly know what he will think sufficient? –  Mariano Suárez-Alvarez Feb 25 '14 at 2:30
@MarianoSuárez-Alvarez There is a small but non-zero probability that one of us is his professor O_O –  Arkamis Feb 25 '14 at 2:30
Some possible topics (assuming you didn't do them), most of which you can find in older texts: envelopes and singular solutions, orthogonal curves and Cauchy-Riemann equations, power series solution method (basics), Laplace transform method of solving ODEs, method of solving Euler equations, obtaining differential equations for various families of curves, issues involved with bodies moving in resisting mediums (frictional force proportional to speed or square of the speed, impact on ballistics and warfare, etc.), variation of parameters (2nd order and 3rd order equations), etc. –  Dave L. Renfro Feb 25 '14 at 17:59

1 Answer 1

The Korteweg–de Vries equation (KdV) equation or the non-linear Schrodinger equation and their solutions might be something that might be of interest.

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