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@jemoka / Jemoka Knowledge Base / wiki/concepts/autonomous_odes.md
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--- 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 “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. See stability (ODEs) time-invariant expressions For forms by which: \begin{equation} y’ = f(y) \end{equation} as in, the expression is time invariant.