Equilibrium solution of an ordinary differential equation
= Equilibrium solution of an ordinary differential equation
{title2=$y(x)\equiv c$}
= Equilibrium solution
{synonym}
A constant <function> $y(x)=c$ is an equilibrium solution of $y'=F(x,y)$ 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>.