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've worked through the book's exercises and wrote up solutions as I went along.
In total, after all solutions are presented, the book as it currently stands is almost 1000 pages long.
You can find the computational exercises (without explanations) for free in the links below. I'm selling the text description of my solutions in PDF format for $75.00 (US dollars) via PayPal (see the link below). While this may seem expensive (and I'm sorry about that) due to the number of problems in each chapter this solution manual has taken many years to finish and was a massive amount of work. In the end, the cost above is small (I think) to the stronger guarantee that your learning the material correctly. Note: After you buy with PayPal you will be automatically directed to a web page where you can immediately download the solution manual.