# 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.

## Functions

## Topics

ODE background information, solver descriptions, algorithms, and example summary.

Usage of `odeset`

and table indicating which options work
with each ODE solver.

Detect events during solution of ODE.

This page contains two examples of solving nonstiff ordinary differential equations using `ode45`

.

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.

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

**Solve System of ODEs with Multiple Initial Conditions**

This example compares two techniques to solve a system of ordinary differential equations with multiple sets of initial conditions.

**Troubleshoot Common ODE Problems**

FAQ containing common problems and solutions.