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?