How do you use Inverse Operators for n'th order DEs?

Actually, I didn't really mean n't order as in generalized forms or anything, just higher order than 1, but not so high as to come computationally ridiculous or require any upper division math major stuff. The final's coming up and I kind of totally forget how to use inverse operators to non-homogeneous solve n'th order differential equations. My teacher taught this method instead of undetermined coefficients to solve certain DE's, I can't find the handout he gave us it isn't in the book or anywhere else on the internet as far as I can find (I'm sure it's there somewhere, I just can't find it). Any information on this subject would be appreciated.

Also, although I don't remember it, this method seemed to be a relatively straightforward method of solving these DEs and my teacher found preferable to undetermined coefficients. It might be a good idea for someone to add this to the Differential Equations Tutorial thread. (Maybe I'll do it after my final if I ever find that handout (Worried) )