A system of ordinary differential equations can often be written in the form [1,2]

where **t** is the independent variable (normally time) and

Equation (1) consists of **n** first-order differential equations.
If the original set of equations is of higher-order, they can often be
transformed to Eq. (1) by redefining variables and expanding their
number.
(It may be recalled that in classical mechanics the **m** second-order
differential equations arising from a Lagrangian formulation are
equivalent to the **n=2m** first-order equations from the Hamiltonian
formulation.)