Built into the Wolfram Language 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. The Wolfram Language'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 — numerical solutions to equations and systems

FindRoot — numerically find local roots of equations

SolveValues, NSolveValues — directly gives solution vectors

AsymptoticSolve — asymptotic approximation to algebraic equations

DSolve — exact solutions to differential, delay and hybrid equations

NDSolve — numerical solutions to differential, delay and hybrid equations

ParametricNDSolve — numerical solution to differential equations with parameters

AsymptoticDSolveValue — asymptotic solutions to differential equations

RSolve — exact solutions to recurrence and functional equations

RecurrenceTable — table of solutions to recurrence and functional equations

AsymptoticRSolveValue — asymptotic solutions to recurrence equations

FindInstance — find particular solutions to equations and inequalities

Reduce — reduce equations and inequalities

LinearSolve — solve linear systems in matrix form

FrobeniusSolve  ▪  LyapunovSolve  ▪  DiscreteLyapunovSolve  ▪  RiccatiSolve  ▪  DiscreteRiccatiSolve

ContourPlot, ContourPlot3D — plot solution curves and surfaces

RegionPlot, RegionPlot3D — plot regions satisfied by inequalities