Undermined Coefficients is a method to solve a nonhomogeneous differential equations and linear systems of differential equations. Given a system in the following form:
where
If we compare this equation against the one given in nonhomogeneous linear system, we see that it is nearly identical, the only difference being that matrix
Thus to solve this equation we must find two solutions:
When working with systems of equations the procedure is roughly the same, given the following equation:
We first find our complementary solution which we can find by solving the matrix
This yields the following eigenpairs:
Which can be rewritten as our complimentary solution:
Now onto our particular solution. We first compare our original equation against our list to find that it matches with entry 3.
incomplete, see diffeq hw 8