My university also has limited Mathematica access/adoption---although we're currently working on a campus license. For all the money we blow on new buildings and new professors to fill them, it's silly not to give them actual tools to use! (especially when the tools are so cheap relative to the cost of a new professor)
1. You get the ball rolling and inquire about a campus wide license. I think the cost per student is likely to be surprisingly low, especially when compared to patchwork licensing or having students purchase or rent Mathematica for the semester. Use this as a selling point when pitching the idea to administrators.
2. In the mean time, rather than waiting for the site license to go through, you can have students purchase their own student version (or rent it---although I believe students will invest more in learning the software if they purchase it outright).
As an example, I taught a junior level economics course with Mathematica (first time using this approach) and required students to purchase a student license (cost ~$130) along with a book called 'Mathematica Navigator' (cost ~$55 new). Because of the significant expense, I told students to get an OLD edition of Intermediate Macroeconomics (the usual macro text I use for the course) from half.com or amazon.com, at a cost of only $5-$10. Using this approach I was still able to save students money, as the 'new' edition of Mankiw would have cost them ~$200. (Prices in Italy may vary---I don't know if world textbook prices are as bonkers as they are in the U.S.)
If you teach diff eq, I virtually guarantee you could come up with a similarly beneficial arrangement for your students. I highly doubt math books change much from version to version. One bit of advice: make sure you show students exactly where they can find the appropriate old editions and tell them to order ASAP.
Finally, I think you'll really enjoy teaching with Mathematica. I also believe incorporating programming into technical courses does students a great service in the long run. Go for it!
(and plan on using the forthcoming version 8... it's light years ahead of version 4.)