---
title: "autonomous ODEs"
type: concept
related: [Stability, Seperable Diffequ, First Order Odes]
source: https://www.jemoka.com/posts/kbhautonomous_odes/
confidence: high
status: active
---

an First Order ODE is &ldquo;autonomous&rdquo; when:
\begin{equation} y&rsquo; = 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.
See stability (ODEs)
time-invariant expressions For forms by which:
\begin{equation} y&rsquo; = f(y) \end{equation}
as in, the expression is time invariant.
