Equilibrium solution of an ordinary differential equation ($y(x)\equiv c$)

A constant function $y(x)=c$ is an equilibrium solution of $y^{\prime }=F(x,y)$ on an interval when $F(x,c)=0$ throughout that interval. Dividing by a factor such as $y-c$ during separation of variables excludes this solution, so it must be checked separately. For an autonomous differential equation, the constant state is an equilibrium point.