This is a beautiful introduction to differential equations. The authors do a great job of introducing both simple and complex concepts. A nice feature of this book is the use of some more advanced mathematics than is typically seen in an introductory course like this one. Readers unfamiliar with this book can see what others have said here.
To learn this material as well as possible I'm working through the book's exercises and wrote up solutions as I went along.
This is a work in progress that currently includes solutions to all questions in Chapters 1-3, 5-6, and 8 (inclusive).
While not the solutions to all problems (yet) the book as it currently stands is almost 760 pages long.