# Ordinary Differential Equations

The Ordinary Differential Equation (ODE) solvers in MATLAB^{®} solve initial value problems with a variety of properties. The solvers can work
on stiff or nonstiff problems, problems with a mass matrix, differential algebraic equations
(DAEs), or fully implicit problems. For more information, see Choose an ODE Solver.

Solve problems and set options using a visual interface with the Solve ODE Live Editor task.

## Objects

`ode` | Ordinary differential equations (Since R2023b) |

`odeMassMatrix` | ODE mass matrix (Since R2023b) |

`odeJacobian` | ODE Jacobian matrix (Since R2023b) |

`odeEvent` | ODE event definition (Since R2023b) |

`odeSensitivity` | ODE sensitivity analysis (Since R2024a) |

`ODEResults` | Results of ODE integration (Since R2023b) |

## Live Editor Tasks

Solve ODE | Solve system of ordinary differential equations in the Live Editor (Since R2024b) |

## Functions

## Topics

**Choose an ODE Solver**ODE background information, solver descriptions, algorithms, and example summary.

**Summary of ODE Options**Usage of

`odeset`

and table indicating which options work with each ODE solver.**ODE Event Location**Detect events during solution of ODE.

**Solve Nonstiff ODEs**This page contains two examples of solving nonstiff ordinary differential equations using

`ode45`

.**Solve Stiff ODEs**This page contains two examples of solving stiff ordinary differential equations using

`ode15s`

.**Solve Differential Algebraic Equations (DAEs)**Solve ODEs with a singular mass matrix.

**Nonnegative ODE Solution**This topic shows how to constrain the solution of an ODE to be nonnegative.

**Troubleshoot Common ODE Problems**FAQ containing common problems and solutions.