We discuss the solution of an th order nonhomogeneous linear differential equation, making use of the method of undetermined coefficients to find a particular solution.

Undetermined Coefficients for Higher Order Equations

In this section we consider the constant coefficient equation

where and is a linear combination of functions of the form or

From Theorem thmtype:9.1.5, the general solution of (eq:9.3.1) is , where is a particular solution of (eq:9.3.1) and is the general solution of the complementary equation In Trench 9.2 we learned how to find . Here we will learn how to find when the forcing function has the form stated above. The procedure that we use is a generalization of the method that we used in Trench 5.4 and 5.5, and is again called method of undetermined coefficients. Since the underlying ideas are the same as those in Trench 5.4 and 5.5, we’ll give an informal presentation based on examples.

Forcing Functions of the Form

We first consider equations of the form

Forcing Functions of the Form

We now consider equations of the form where and are polynomials.

Text Source

Trench, William F., ”Elementary Differential Equations” (2013). Faculty Authored and Edited Books & CDs. 8. (CC-BY-NC-SA)