Undermined Coefficients for Systems of Linear Equations

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 is no longer a function. This means that our general solution takes the form as specified in the above file.

Thus to solve this equation we must find two solutions:

Examples

Example 2

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 the same way we would with a linear system of differential equations.

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