autonomous ODEs

an First Order ODE is “autonomous” when:

\begin{equation} y’ = f(y) \end{equation}

for some \(f\) of one variables. Meaning, it only depends on the independent variable \(t\) through the use of \(y(t)\) in context.

This is a special class of seperable diffequ.

autonomous ODEs level off at stationary curves

for autonomous ODEs can never level off at non-stationary points. Otherwise, that would be a stationary point.

For forms by which:

\begin{equation} y’ = f(y) \end{equation}

as in, the expression is time invariant.