# Documentation

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# Ordinary Differential Equations

Ordinary differential equation initial value problem solvers

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

 `ode45` Solve nonstiff differential equations — medium order method `ode23` Solve nonstiff differential equations — low order method `ode113` Solve nonstiff differential equations — variable order method
 `ode15s` Solve stiff differential equations and DAEs — variable order method `ode23s` Solve stiff differential equations — low order method `ode23t` Solve moderately stiff ODEs and DAEs — trapezoidal rule `ode23tb` Solve stiff differential equations — trapezoidal rule + backward differentiation formula
 `ode15i` Solve fully implicit differential equations — variable order method `decic` Compute consistent initial conditions for ode15i
 `odeget` Extract ODE option values `odeset` Create or modify options structure for ODE solvers
 `deval` Evaluate differential equation solution structure `odextend` Extend solution to ODE

## Topics

Choose an ODE Solver

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

Summary of ODE Options

Table indicating which options of `odeset` 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.