Example 5.  Use the matrix exponential to find the general solution for the system of  D.E.'s   ,  where
    .  

Solution 5.

A fundamental matrix solution is   .

The matrix exponential is  .

The solution to the D. E. with initial conditions  ,   is  .  

We are done.

Aside.  We compare the above work, with the construction of    using Mathematica's subroutine  MatrixExp.

(c) John H. Mathews 2004