Autonomous Differential Equation

A differential equation for which $dy/dx$ is a function of the dependent variable (here further adressed as $y$) only is called an autonomous differential equation.

Equilibrium values

The values of $y$ for which $dy/dx=0$ are called equilibrium values or rest points.

• A point is a stable equilibrium if the values of $y$ near it tend to this value.
• A point is a unstable equilibrium if the values of $y$, if not exactly that value, will tend to distance themselves from it.