Ordinary differential equation

This is how we describe motion in the Euclidean space. It is given by an ordinary differential equation (ODE): $$x'(t)=f(x(t)),$$ where $f:{\bf R}^n \to {\bf R}^n$ is a continuous vector field and $x:I \to {\bf R}^n$ is a differentiable parametric curve defined on an open interval $I$.