based on an earlier version of the Wolfram Language.
Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically accessed through a small number of exceptionally powerful functions. Mathematica's symbolic architecture allows both equations and their solutions to be conveniently given in symbolic form, and immediately integrated into computations and visualizations.
Solve — exact solutions to equations and systems
NSolve — general numerical solutions to equations and systems
FindRoot — numerically find local roots of equations
DSolve — exact solutions to differential equations
NDSolve — numerical solutions to differential equations
RSolve — exact solutions to recurrence and functional equations
RecurrenceTable — table of solutions to recurrence and functional equations
FindInstance — find particular solutions to equations and inequalities
Reduce — reduce equations and inequalities
LinearSolve — solve linear systems in matrix form