Homogeneous Equations

Author: John J Weber III, PhD Corresponding 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}}$$n^{\text{th}}$-degree homogeneous linear ODEs.

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

Homogeneous Equations

Solutions to Homogeneous Equations

Activity 02

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

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Last Modified: Monday, 6 September 2020 17:33 EDT