An Introduction to Ordinary Differential Equations (Universitext)
Ravi P. Agarwal, Donal O'Regan
My first grad ODE course used this book. The book contains a very concise presentation of the material. It has a bit of an odd layout, with each section covering a single lecture (42 total), but it works well as it is arranged more or less the way the material should be covered. Every section has exercises and the solutions or hints to nearly every problem are available, very good for learning from the book.
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The book removed at the request of the copyright holder.