have word 2013 but need 2010

The question is rather whether you can buy 2010, since it is no longer easily available at retail. If the university course requires Word 2010, then (in my view, at least) it is the responsibility of the university to make Office 2010 available for purchase at a student price.

In what way is Word 2013 not compatible with your coursework? I know some users have problems getting the document themes required by certain textbook exercises (because MS keeps changing them with every version), but other users here have kindly offered to provide the .thmx files required for given themes.

Word 2013 is compatible with previous Word versions, in the sense that it supports all of their features. Word 2013 does some things a bit differently, though, and some user options found in earlier versions have been deprecated. As well, some 3rd-party addins, such as 'Write-N-Cite' are yet not compatible with Word 2013. So, unless you're required to use out-dated addins or superseded themes as Suzanne mentions, you shouldn't have any particular issues.

You can still buy Office 2010 new (or 2nd-hand) on ebay or at, say: http://www.amazon.com/Microsoft-Office-Home-Student-2010/dp/B003FO8956/ref=sr_1_6.