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Название: An Introduction to Ordinary Differential Equations (Dover Books on Advanced Mathematics)
Автор: Coddington E.
and one can learn to go the first steps in ODEs. BUT ... the book is taylored very much to the american market meaning that even bloody beginners can understand it. Hence, it does not go very far and stays elementary throughout. If you really want to take off read the book which the author wrote with Levinson (Theory of Ordinary Differential Equations).