# Studying ODEs… is it worth it?

I am a first year Master's student in applied mathematics. I'm currently taking a Mathematical Physics class and we have been studying techniques for solving ODEs. There is some overlap with undergrad ODEs.

Solving these problems (ex: $x^2y''+xy'-16y=8x^4$) often takes lots of time and lots of algebraic manipulation, all to find a solution that I won't use.

I understand that it is important to become familiar with these equations and have an idea about how they are solved. But I am failing to see the big picture.

How will knowing myriad solution techniques for these ODEs help my future research in applied mathematics?

Have you found this knowledge useful in your research?

• This famous essay by Gian Carlo Rota can be an interesting read for you. – Giuseppe Negro Dec 3 '17 at 18:26
• "Myriad solution techniques" : maybe 50 or 100 years ago... But nowadays, it"s far from that, in particular with computers. You well never be an "applied mathematician" without a good background in this very fundamental (and rewarding) field... – Jean Marie Dec 3 '17 at 18:27
• @GiuseppeNegro That was a very fascinating read. Unfortunately, it damps my motivation to study for the final exam! :) – EternusVia Dec 3 '17 at 18:58
• @EternusVia: Dang! :-) I am sorry. The opposite is true: a solid knowledge of ODEs is something that I would have found very useful during my PhD studies. – Giuseppe Negro Dec 3 '17 at 19:02