---
title: "phase line"
source: https://www.jemoka.com/posts/kbhphase_line/
---

\begin{equation} y&rsquo; = f(y) \end{equation}
for autonomous ODEs, we can plot a phase line
because autonomouse ODEs, we can plot such a line whereby we can analyze the direction of a solution function&rsquo;s travel
a particle&rsquo;s one-way motion must converge to a stationary value, or \(\pm \infty\), as \(t\) increases
