I am now planning to self-study ODE, and I want a textbook that explains things clearly. After searching on this site, I find three books that are frequently reccommended: 1.Tenenbaum & Pollard 2.Coddington 3.F.Simmons
However, I would like to know the difference between these books. Are they at the same level? Or do they focus more on theory or on computation?
Also, I want a book that deals with numerical solutions (not just having one chapter on it).
I would recommend Hairer, Norsett, Wanner Solving Ordinary Differential Equations I (Springer).
It is very numerical-oriented but its first chapter (120 pages!) deals with the theory of ODEs.