Author: John J Weber III, PhDCorresponding Textbook Sections:

Section 4.2 – Homogeneous Linear Equations: The General Solution

Expected Educational Results

Objective 10–1: I can identify if two or more functions are linearly-independent.

Objective 10–2: I can identify the characteristic equation for ${n}^{\text{th}}$-degree homogeneous linear ODEs.

Objective 10–3: I can find the most general solution to ${n}^{\text{th}}$-degree homogeneous linear ODEs.

Homogeneous Equations

Solutions to Homogeneous Equations

Activity 02

Let $y={e}^{rt}$, find all values for $r$ such that $y={e}^{rt}$ are solutions to $a{y}^{{\textstyle \phantom{\rule{0.167em}{0ex}}}\prime \prime}(t)+b{y}^{{\textstyle \phantom{\rule{0.167em}{0ex}}}\prime}(t)+cy(t)=0$. Explain.