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.