Variation of Parameters

Variation of ParametersExpected Educational ResultsVariation of ParametersDefinition: Particular SolutionDefinition: Variation of ParametersDefinition: General SolutionMethod of Variation of ParametersInvestigation 02CC BY-NC-SA 4.0

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

Expected Educational Results

Variation of Parameters

Definition: Particular Solution

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

Definition: Variation of Parameters

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 .

Definition: General Solution

.

Method of Variation of Parameters

NOTE: The terms determined by the method of variation of parameters must be linearly independent of the terms in .

  1. Find two linearly independent solutions to the corresponding homogeneous equation.

  2. Let , for some functions and .

  3. Solve for :

  4. Solve for :

  5. The particular solution is .

  6. Write the general solution, .

Investigation 02

Solve the following DEs:

  1. ,

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Last Modified: Thursday, 8 October 2020 7:38 EDT