Solve algebraic and differential equations

You can solve algebraic equations, differential equations, and differential algebraic equations (DAEs).

Solve **algebraic equations** to
get either exact analytic solutions or high-precision numeric solutions.
For analytic solutions, use `solve`

, and for numerical
solutions, use `vpasolve`

. For solving linear equations,
use `linsolve`

. These solver functions have the flexibility
to handle complicated problems. See Troubleshoot Equation Solutions from solve Function.

Solve **differential equations** by
using `dsolve`

. Create these
differential equations by using symbolic functions. See Create Symbolic Functions.

Solve **differential algebraic equations** (DAEs)
by first reducing their differential index to `1`

or `0`

using Symbolic Math
Toolbox™ functions,
and then using MATLAB^{®} solvers, such as `ode15i`

, `ode15s`

,
or `ode23t`

. See Solve Differential Algebraic Equations (DAEs).

Solve Symbolic Equation | Find analytic solutions of symbolic equations in Live Editor |

Solve equations, return full solutions, and visualize results.

**Solve System of Algebraic Equations****Troubleshoot Equation Solutions from solve Function****Solve Equations Numerically****Solve System of Linear Equations****Select Numeric or Symbolic Solver****Solve Parametric Equations in ReturnConditions Mode****Solve Algebraic Equation Using Live Editor Task**

Solve a differential equation analytically by using the `dsolve`

function, with or without initial conditions.

**Solve a System of Differential Equations****Solve a Second-Order Differential Equation Numerically****Solving Partial Differential Equations**

**Solve Differential Algebraic Equations (DAEs)**

This example show how to solve differential algebraic equations (DAEs) by using MATLAB® and Symbolic Math Toolbox™.