Page 106 - Schaum's Outline of Differential Equations

CHAPTER 10

nth-Order Linear

Homogeneous

Differential Equations

with Constant

Coefficients

THE CHARACTERISTIC EQUATION

The characteristic equation of the differential equation

with constant coefficients « ; (/ = 0. , .... n - 11 is
I

The characteristic equation (102) is obtained from (JOJ) h> replacing y'" h\ A/ (./ = 0. I, ... , n— i.
l
Characteristic equations for differential equations 1 having dependent variables other than rare obtained analo-
gously, by replacing inejin deri\alive of the dependent variable b\ A.' (j = 0. I n - I).

4
3
3
(4
Example 10.1. The characteristic equation of y ' - 3y'" + 2y" - v = 0 it, A. - 3A, + 2X - I = 0. The tharaL-terislii;
i."i| nation of

is
Caution: Characteristic equations are onf\ defined for linear homogeneous differential equations with
constant coefficients.

89
Copyright © 2006, 1994, 1973 by The McGraw-Hill Companies, Inc. Click here for terms of use.