In the fall I will be teaching an intro to diff.eq.s course for undergrad engineers. The usual textbook is $150 with solution manual and it's not that great. There must be a cheaper alternative that's just as good. Any help would be greatly appreciated.

I cut my teeth on an 80's version of Differential Equations and Their Applications: An Introduction to Applied Mathematics by Martin Braun . Amazon lists copies as going for under $50. Perhaps someone from this millenium can say if the new editions are still good. I liked the anecdote about the Tacoma Narrows Bridge, and found many of his examples well motivated. Gerhard "Ask Me About System Design" Paseman, 2010.04.15 


I could do worse than to direct you to Dover Publications. They have at least half a dozen introductory differential equation books, all for less than $50. This one has good reviews and it's only $25: Ordinary Differential Equations by Morris Tenenbaum & Harry Pollard http://store.doverpublications.com/0486649407.html 


Ordinary or Partial differential equations? It may also help if you tell us what the outrageously expensive book is so we can better recommend a book of similar level. (You are not speaking of Birkhoff and Rota, are you? I know that one is about the price you listed.) For ODEs, I'd recommend V.I. Arnold's book, it is a classic and under USD30 on Amazon for the paperback edition. Slightly more expensive is Philip Hartman's book, which also covers more material. I bought it many years ago, new, for under USD40, so I am not quite sure what's up with Amazon now that the Hardcover is listed for USD38, while the paperback for close to USD70. For PDEs, McOwen's Partial Differential Equations: Methods and Applications is not bad at USD60, though its 1st order nonlinear system section is a little bit confusing. (A bit of meta gripe: using multiple dollar signs in one paragraph seems to trigger math mode when it really oughtn't, which is why I wrote "USD" above for U.S. Dollars.) 


The best undergraduate introduction to differential equations I knowwhich would be wonderful for your course and you could probably get second hand cheapis George Simmons' DIFFERENTIAL EQUATIONS WITH HISTORICAL NOTES AND APPLICATIONS.It's not too rigorous (although it's done carefully),has lots of applications and even better,it's one of the most beautifully written mathematics books ever published.It almost reads like a novel,with Simmon's wonderful humor and amazing knowledge of the history of the subject. It really makes the subject come alive and your class will love it. Don't get the revision with Steven G. Krantz. Not only is it a lot more expensive,that book is a lot more formal and a lot of Simmons' personal touch that made the first one a classic is utterly missing here. Get either the first or the second edition of the original. 


my favorite ode books for teaching are the ones by either tenenbaum and pollard, or martin braun. these are cheap and excellent. of course arnol'd is incredible but at a higher level. good for me and you, perhaps. 


If the students at your College/University own the Stewart Calculus book, chapters 9 and 17 are probably a good place to start. Or at least to suggest as a supplement to the primary text you choose. 


Wow, how did this old question get resurrected? Anyway, there is something I don't see in any of the other answers, so I'll chime in: Unlike Calculus, one of the problem I find with the Diff Eq is that there is no canonical syllabus. So unless U of Saskatchewan does have a very fixed syllabus for the course, the first step is to decide what "flavor" of course you want. For instance, I had a look at a few of the Dover books, but they seem weak if you want a more "modern" (i.e. technologybased / more pictures) approach to ODE's. Which BTW might be the right way to go especially for engineers. I have yet to find a book that fits my needs, not have I managed to completely pin down what the ideal syllabus should be. 

