2 years later, I understand this answer might not be helpful to you, lamdbafunctor, but for all of the other undergrads who come here and will see this, I believe Boyce and DiPrima's "Elementary Differential Equations and Boundary Value Problems" is exactly what you are looking for. The initial 4 chapter sequence this book follows (First order linear and nonlinear -> Second order linear and nonlinear -> Higher order linear and nonlinear) allows you to see the basic fundamentals being extended to more and more general cases and with very terse yet thorough and meaningful explanations through the entire way, it was a joy to read. From what I saw, it was almost like the book was written explicitly for self-study, as there is very little assumed detail. Many engineers find the downside to this book to be the almost complete lack of real-world modeling examples and such, and my response to them is that the purpose of Boyce/DiPrima is to gain a firm grounding in theory, while the purpose of other books like Edwards/Penney is to gain a firm grounding in physical/real-world applications. I am currently finishing up my first semester in Honors Diff Eq sophomore year, and I owe it almost entirely to this book.

If it lends any credibility to the argument, KhanAcademy's Sal Khan mentioned this was the book he was taught from when he learned diff eq's at MIT, and his selection of videos compliment this book perfectly: http://www.khanacademy.org/math/differential-equations