---
title: "SU-MATH53 JAN172024"
source: https://www.jemoka.com/posts/kbhsu_math53_jan172024/
date: 2024-01-17
---

Key Sequence Notation New Concepts tying into Separated Equations: \(y&rsquo; = f(t,y)\) which are the most nicest. Recall that there was two special cases: seperable and autonomous ODEs. if we can write in terms of elementary function, good times if we can&rsquo;t do it in terms of elementary functions, we can use qualitative analysis t(slope field, etc.) recall again Newton&rsquo;s Law of Cooling phase line and stability (ODEs) Important Results / Claims autonomous First Order ODEs&rsquo; solutions do not cross; as in, if there are two solutinos \(y_1\) and \(y_2\), their curves never intersect. one and exactly one solution exist for every point of an IVP autonomous ODEs level off at stationary curves Questions Interesting Factoids
