I'm really curious about some of the algebra behind ODE's and other seemingly-separate areas of math. For example, I always thought it was kind of arbitrary that, for an n-th order linear homogeneous ODE, the solution space is generated a linear combination of n linearly independent functions.
I'm not much of an algebraist, or whatever the proper term is, but I'd like to start looking into that side of things. I've only read the first few chapters of Artin -- would that text elaborate on some of these issues? Would Pinter suffice? I'm looking for something I could hopefully get through somewhat quickly, if possible.
I'd take a look at Galois Theory of Linear Differential Equations by Put and Singer. You can find it on libgen. The first chapter is pretty easy to read (barring a few things, but you should be able to understand most of it if you've gone through Artin). If you want a more focused expository paper with examples, but few proofs, you could look for "A First Look at Differential Algebra" by Hubbard and Lundell.
