Variation of ParametersExpected Educational ResultsVariation of ParametersDefinition: Particular SolutionDefinition: Variation of ParametersDefinition: General SolutionVariation of Parameters for Higher Order Linear DEsInvestigation 03CC BY-NC-SA 4.0

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

**Section 4.6**-- Variation of Parameters

**Objective 13–1**: I understand when variation of parameters is required to find particular solutions to nonhomogeneous equations.**Objective 13–1**: I can use variation of parameters to find particular solutions to nonhomogeneous equations.

A solution to a nonhomogeneous DE is called the **particular solution**, .

**Variation of parameters** is a more general method to find .

Variation of parameters is used for nonhomogeneous solutions when contains factors or terms other than , , , and .

.

- Identify the homogeneous solution to the -order ODE, i.e., for linearly independent set of solutions .
- The particular solution is for some functions , , , and .
- Find the Wronskian .
- Find the Wronskian , for
**NOTE**: The column and the last row are deleted before calculating the Wronskian on the right side of the definition of ]. - Then the particular solution is

Use the method of variation of parameters to find the general solution to the following DEs:

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**: Thursday, 8 October 2020 7:38 EDT