What is a good book for ordinary differential equations?

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The question is sujestive, I need to know what are good books for learning ordinary differential equations but in a deep mathematical framework. I need names of books that do not focus just on solving particular equations but develop the strong theory around them.

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To get a feel for the subject beyond basic computations, I'd recommend Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch and Smale

Now, for a fully rigorous ODE course, I'd look to Theory of Ordinary Differential Equations by Coddington and Levinson.