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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).

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    $\begingroup$ Exploring ODEs by Trefethen et al. might be a good complement, though surprisingly for a book by a renowned numerical analyst it’s very light on numerics. Still, it’s great on intuition and very clearly written. Also it’s free, so that’s never hurt people.maths.ox.ac.uk/trefethen/ExplODE $\endgroup$
    – eepperly16
    Sep 23, 2019 at 5:14

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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.

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