Let $n\in\mathbb{N}$, let $U\subset \mathbb{R}^n$ be a set, let $f:U\to \mathbb{R}^n$ be a map, and let $x^*\in U$. For every nonempty interval $J\subset \mathbb{R}$, define the constant curve $x_J:J\to U$ by $x_J(t)=x^*$ for all $t\in J$. Interpret a solution on $J$ as follows: if $J$ has at least two points, the curve satisfies the differential equation at every interior point of $J$ and, when an endpoint belongs to $J$, satisfies it there with the corresponding one-sided derivative; if $J$ is a singleton interval, no differential equation is imposed. Then $x_J$ solves the autonomous [ordinary differential equation](/page/Ordinary%20Differential%20Equation) $\dot{x}(t)=f(x(t))$ on every nonempty interval $J\subset \mathbb{R}$ if and only if $x^*$ is an equilibrium point of the vector field $f$, that is, $f(x^*)=0$.