Solve ordinary differential equations and systems
of such equations

An ordinary differential equation (ODE) contains derivatives
of dependent variables with respect to the only independent variable.
If `y`

is a dependent variable and `x`

is
an independent variable, the solution of an ODE is an expression `y(x)`

.
The order of the derivative of a dependent variable defines the order
of an ODE.

When solving an ODE, use symbolic functions to specify dependent
variables. For example, `syms y(x)`

creates the symbolic
function `y`

of `x`

, and the variable `x`

.
See Create Symbolic Functions for details. Construct an
ODE by using `diff`

to denote
derivatives and `==`

to
create an equation. If an ODE has initial or boundary conditions,
specify them as additional equations. Then use `dsolve`

to
solve an ODE.

dsolve | Ordinary differential equation and system solver |

massMatrixForm | Extract mass matrix and right side of semilinear system of differential algebraic equations |

odeFunction | Convert system of symbolic algebraic expressions to MATLAB function handle suitable for ode45, ode15s, and other ODE solvers |

odeToVectorField | Convert higher-order differential equations to systems of first-order differential equations |

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