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
ContourPlot,
ContourPlot3D — plot solution curves and surfaces
RegionPlot,
RegionPlot3D — plot regions satisfied by inequalities
