## Select Numeric or Symbolic Solver

You can solve equations to obtain a symbolic or numeric answer. For example, a solution to $\mathrm{cos}\left(x\right)=-1$ is `pi` in symbolic form and `3.14159` in numeric form. The symbolic solution is exact, while the numeric solution approximates the exact symbolic solution. Symbolic Math Toolbox™ offers both symbolic and numeric equation solvers. This table can help you choose either the symbolic solver (`solve`) or the numeric solver (`vpasolve`). A possible strategy is to try the symbolic solver first, and use the numeric solver if the symbolic solver is stuck.

Solve Equations Symbolically Using solveSolve Equations Numerically Using vpasolve
Returns exact solutions. Solutions can then be approximated using `vpa`.Returns approximate solutions. Precision can be controlled arbitrarily using `digits`.
Returns a general form of the solution.For polynomial equations, returns all numeric solutions that exist. For nonpolynomial equations, returns the first numeric solution found.
General form allows insight into the solution.Numeric solutions provide less insight.
Runs slower.Runs faster.
Search ranges can be specified using inequalities.Search ranges and starting points can be specified.
`solve` solves equations and inequalities that contain parameters.`vpasolve` does not solve inequalities, nor does it solve equations that contain parameters.
`solve` can return parameterized solutions.`vpasolve` does not return parameterized solutions.

`vpasolve` uses variable-precision arithmetic. You can control precision arbitrarily using `digits`. For examples, see Increase Precision of Numeric Calculations.