Homogeneous System of Three Coupled, First-Order, Linear Differential Equations
This Demonstration calculates the eigenvalues and eigenvectors of a linear homogeneous system and finds the constant coefficients of the system for a particular solution. The sliders let you vary the initial conditions.
This Demonstration comes from , Section 6.2, Systems of First Order Equations, Example 3.
 J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, 2nd ed., New York: John Wiley and Sons, 2010.