First Order Systems

Important for numerical work. Library subroutines usually do not solve higher order equations, but they do solve first order systems.

General First Order System:

Written out

If the functions are linear constant coefficient ones, we can rewrite this as:

In this class, solution using eigenvalues and eigenvectors is required. We assume that A is diagonalizable.

Homogeneous solution:

where are the eigenvalues of A and the eigenvectors.

General solution: Guess and add a particular solution. Varying the parameters C₁, C₂, ... also works.