Differential Equations: Second-Order ODEs and Characteristic Equations
Автор: Alann Rosas
Загружено: 2026-01-18
Просмотров: 2
In this video, we solve Exercises 2.2.7, 2.2.8, and 2.2.11 from Jiří Lebl's "Notes on Diffy Qs: Differential Equations for Engineers". Each of these exercises gives us a second-order, linear, homogeneous, constant-coefficient ODE whose solutions are found by solving the corresponding characteristic equation. Exercises 2.2.7, 2.2.8, and 2.2.11 have characteristic equations with two real roots, one repeated root, and two complex roots, respectively, so we get practice with the three types of solution families to expect from these types of ODEs.
0:00 Problem statements
0:54 First ODE
3:21 Second ODE
6:38 Second ODE, solving for constants
10:27 Third ODE
Link to Jiří Lebl's notes: https://www.jirka.org/diffyqs/
12:23 Third ODE, finding roots with the quadratic formula
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