Example 2.  Use the matrix exponential to find the general solution for the system of D. E.'s   
            

Solution 2.

First, write the system in vector and matrix form  .

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