Equilibrium Solution

Definition of Equilibrium Solution:

*Created on 21:29 09-01-2024

An equilibrium solution is a constant solution $y(t)=c$ to the ODE

$$\frac{dy}{dt}=f(t,y)$$

The graph of an equilibrium solution is a horizontal line. Such a line has a slope of zero, i.e., $y^{\prime }=0$. This can only happen if $f(t,y)=0$ has a solution $y=c$ for some real constant $c$.