Module for the Method of Variation of Parameters

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Background.

    Use Mathematica to implement the method of undetermined coefficients to find the general solution to the following differential equations. Then find the solution to the D. E. with the given initial conditions and plot it.

Example 1. (a) Use the method of variation of parameters to find the general solution to the D. E.  

    .  

Example 1. (b)  Find the solution  with the I.C.'s  

    ,  

and plot this solution over the intervals   and  .  

Example 2. (a)  Use the method of variation of parameters to find the general solution to the D. E.  

    

Example 2. (b)  Find the solution  with the I.C.'s  

    ,  

and plot this solution over the interval  .

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