Variation of Parameters

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:

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

.

Variation of Parameters for Higher Order Linear DEs

  1. Identify the homogeneous solution to the -order ODE, i.e., for linearly independent set of solutions .
  2. The particular solution is for some functions , , , and .
  3. Find the Wronskian .
  4. 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 ].
  5. Then the particular solution is

Investigation 03

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

CC BY-NC-SA 4.0

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