Module for the Generalized Eigenvector Solution in a Linear System of O. D. E.

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

Background.

    The matrix    has   as an eigenvalue, with the associated eigenvector provided  ,  and the eigenvector corresponding to    is a non-zero solution to  .  Generalized eigenvectors will be of the form  

    ,
    and
    .

Example 1. Use eigenvectors and eigenvalues to solve the differential equation system    where  .  

Example 2 (a) Find the general solution to the system of  D.E.'s  , where

      

2 (b) Find the solution in (a) that has the I.C.'s

    ,

and plot the solutions over the interval  .

Example 3 (a) Find the general solution to the system of  D.E.'s  , where

      

3 (b) Find the solution in (a) that has the I.C.'s

    ,

and plot the solutions over the interval  .