This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Equation Solving
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
TUTORIALS