Mathematica is a computer algebra system that is widely used in science, engineering, mathematics, finance, and other fields. MATLAB also has a symbolic algebra package, but Mathematica's symbolic computation facilities are more sophisticated and integrated with the rest of its features.
Mathematica has the ability to analytically and numerically solve differential equations using the DSolve and NDSolve commands. As a result, it can an indispensable tool for an instructor wanting to check or generate examples or problems.
Mathematica is not designed primarily for educational purposes, and its LISP-inspired syntax creates a steep learning curve for students and instructors alike. However, since it is widely used in academia and industry it may be beneficial for students to become familiar with its capabilities.
Instructors may find the Manipulate command in Mathematica an especially helpful tool for creating interactive tools for exploring differential equations. The Wolfram Demonstrations Project contains a large number of interactive tools built with the Manipulate (and related) commands.