Differential Equations Reference Request

Try Birkhoff/Rota and Hirsch/Smale (I actually don't know the latest edition with Devaney).

"Theory of Ordinary Differential equations" by Coddington. If you find the previous one advanced, there is "An Introduction to Ordinary Differential Equations" by Coddington too. The first one is very complete and have a lot of things that I have never seen in other books. The second one is very basic (there is almost no qualitative theory), but proves the validity of some techniques usually used to solve ordinary differential equations. They also gives some explicit formulas for solution in special cases.Carmen Chicone's book "Ordinary Differential Equations with Applications" is good too if you want to study better the qualitative theory.

I would recommend Differential Equations, Mechanics, and Computation You can read first pages to figure out whether it works for you. The book is 1) introductory, 2) rigorous, 3) with emphasis to physics.