Complementary Solutions to Linear Systems

The complementary solution to a linear system differential equation is found by the following:

1. Is the linear system homogeneous? If not make it homogeneous by removing and setting it equal to zero.
2. Solve the system the same way you would for any other linear system of differential equations.

If the linear system was homogeneous then we have found our general solution, if not then we need to find a particular solution to the system.