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