# Autonomous system (mathematics)

In differential equations, an autonomous system is an equation of the form

[itex]\frac{d}{dt}x(t)=f(x(t))[itex]

where x takes values in n-dimensional Euclidean space and t is usually time. It is distinguished from systems of differential equations of the form

[itex]\frac{d}{dt}x(t)=g(x(t),t)[itex]

in which the law governing the rate of motion of a particle depends not only on the particle's location, but also on time; such systems are not autonomous.

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