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Rating: 
Summary: Good material, but falls short with examples
Review: I'm not the greatest math student, but I certainly manage to get along. Differential equations has thus far easily been the most annoying math class I've taken (multivariable calculus was a cakewalk). However, I am the kind of person that likes to look at problems which are solved out for me, and apply the procedure to whatever I am working on. While this book certainly provides many examples, it fails to provide some where critically needed. That is my main gripe with this book, and since it causes difficulty in my grasping of the material, that is why it loses two stars. However, the order of presentation of the material is adequate, and it is overall a very well paced textbook. If you have a good instructor or have some other way of obtaining help outside from this book, it serves as a wonderful companion resource. I have no experience with other differential equations textbooks, but I would recommend looking into a textbook with better examples (there's so little information on how to solve an oscillating system with an external force). Other than that, this is fine.
Rating:
Summary: booooo!
Review: Not too good... there weren't enough examples as others said, and some of the derivations were unnecessarily complicated. Try the book by Rainville & Bedient instead, if it's still in print.
Rating: 
Summary: The best mainstream ODE text
Review: This is the best mainstream book on (ordinary) Diff. Eqns. It is mainly oriented to engineers but a math major could benefit from it as well. Like most books on this subject it emphasizes on solving relatively small classes of Diff. Eqns, namely those that can be solved in closed form and like most of those books avoids, but not completely, the qualitative study of the subject. However, I believe that this is the best compromise of a "recipe book" and a book that really tries to encourage understanding of the subject. The book suffers from too many examples and pictures. The examples take too much space and have too many details. I can hardly blame the authors for this - they, and the publisher, just want to sell more books, and they have therefore to follow the general trend. You either have to write a book like this, or a real one, like Arnold's book, but that would be a book for a few only. "Proof" in Boyce-DiPrima is a dirty word but so is in any other mainstream text on Diff. Eqns. It was interesting to me to read most of the negative reviews here. Poor mathematical background makes many readers believe that the exercises are hard, the answers are put in weird form (meaning the reader has problems with middle school algebra), etc. If anything, many of the exercises are too easy. Those, who need Mathematica for solving integrals - you'd better retake your Calculus course. There are very few examples that really require Mathematica and they are mentioned clearly. Really interesting and challenging problems can be found sometimes but authors clearly understand that too many of those would hurt the sale numbers. One reader wrote: "This book makes ODEs and PDEs look much more difficult than they really are. " Well, like many other books, this book does not give you the slightest idea what ODEs and PDEs really are (try John's book as an introduction to PDEs), they are far more intellectually challenging and deep that most students can imagine. After so much negative comments, why do I still think that this is a good book? Because you cannot beat the system, at least this is not the way, and the math culture of most readers and students is not adequate to appreciate a real book (try Arnold). If you want a book that is still readable by the majority of the undergrad students, then this is the best one. If you want a real one, look elsewhere but do not complain that the author does not show the steps when solving a quadratic equation.
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