Variable Coefficient Equations

Variable Coefficient EquationsExpected Educational ResultsVariable Coefficient EquationsHigher-Order Cauchy-Euler EquationsInvestigation 06CC BY-NC-SA 4.0

Author: John J Weber III, PhD Corresponding Textbook Sections:

Section 4.7 – Variable Coefficient Equations

Expected Educational Results

Objective 14–1: I can identify variable-coefficient equations.
Objective 14–2: I can find a solution to a homogeneous Cauchy-Euler equation.
Objective 14–3: I can find a solution to a nonhomogeneous Cauchy-Euler equation.
Objective 14–4: Given a solution, I can apply the Reduction of Order Theorem to find another solution to a Cauchy-Euler equation.
Objective 14-5: I can find a solution to a Cauchy-Euler IVP.

Variable Coefficient Equations

Higher-Order Cauchy-Euler Equations

NOTE: You will not be assessed on solving third-order [or higher] Cauchy-Euler Equations.

Investigation 06

NOTE: You will need to derive the characteristic equation using a similar derivation as shown in Activity 02.

$\displaystyle t^3 y^{\,\prime\prime\prime}-6t^2 y^{\,\prime\prime}+19ty^{\,\prime}-27y=0$ $t>0$ .

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Wednesday, 14 October 2020 11:45 EDT