A system of ordinary differential equation is autonomous when it does not depend on time (does not depend on the independent variable) i.e. $\dot{x}=f(x)$ . In contrast nonautonomous is when the system of ordinary differential equation does depend on time (does depend on the independent variable) i.e. $\dot{x}=f(x,t)$ .

It can be noted that every nonautonomous system can be converted to an autonomous system by adding a dimension. i.e. If $\dot{{x}}={f}({x},t)$ ${x} \in \mathbb{R}^n$ then it can be written as an autonomous system with ${x} \in \mathbb{R}^{n+1}$ and by doing a substitution with $x_{n+1} = t$ and $\dot{x}_{n+1}=1$ .