Homogeneous Equations

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

Expected Educational Results

Constant Coefficients Method

  1. Identify the characteristic equation for the homogeneous linear DE.

  2. Completely solve the characteristic equation.

  3. Use the roots of the characteristic equation for the homogeneous, yh(t), solution.

Investigation 05

Solve the following nth-order homogeneous ODEs using linear combination of n linearly-independent solutions:

  1. y6y+9y=0

  2. y+3y+2y=0

  3. y=4y

  4. 3y4y+y=0

  5. y5y6y=0

  6. y25y=0

  7. y(5)(t)8y(t)+2y(t)+15y(t)10y(t)=0

Solve Polynomial Equations

Use Technology to Find Roots of Characteristic Equations

Mathematica

Use Technology to Verify Solutions to nth-order homogeneous ODEs

Warnings:

  1. Be very careful with the syntax. Syntax is the set of rules on how to write computer code. Every software program has its own unique syntax. Some basic Mathematica syntax is located at: http://www.jjw3.com/TECH_Common_Functions.pdf.

  2. To execute code (including comment codes), press and hold the SHIFT key and press the ENTER key.

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