ODE book recommendation

I have just completed my first year study and know elementary analysis and a little bit functional analysis. I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?

Solution 1:

A classical theoretical book on ODE is Hartman.

A very good book, and slightly less demanding than Hartman is Hale's book

A geometric picture of differential equations is given in two Arnold's books: one and two

ODE from a dynamical system theory point of view are presented in Wiggins' book

Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.

The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.

Solution 2:

You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.

Solution 3:

You can try this one also...

'Differential Equations Theory, Technique and Practice' by G. F. Simmons & S. G. Krantz (McGraw Hill Higher Education)