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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?

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    Its not an ODE book, and it be heavy going at an early stage, but I like the (brief) treatment of ODEs in Kantorovich & Akilov's "Functional Analysis". In particular, it provides a fixed-point scheme (as in Picard) that is useful for showing continuity of solutions with respect to parameters.2012-07-27

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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.

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    @Leo$n$idKovalev Ups. Somehow I understood that OP asked about a _second_ course in differential equations. I update my post.2012-07-29
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You might try Birkhoff and Rota or Lefschetz or Nemytskii and Stepanov.

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You can try this one also...

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