Page 259 - Schaum's Outline of Differential Equations

CHAPTER 24

Solutions of

Linear Differential

Equations with

Constant Coefficients

by Laplace Transforms

LAPLACE TRANSFORMS OF DERIVATIVES
Denote ^{v(.v)| h\ Y(.i). Then under broad conditions, ihe Laplace transform of the «th-deri\ alive
(n= 1.2,3. ...) of yU) is

If Ihc initial conditions on v(.v) at x = 0 arc given by

then (24.1) can be rewritten as

For the special cases of n = I and /? = 2. Eq. (24.3) simplifies to

242
Copyright © 2006, 1994, 1973 by The McGraw-Hill Companies, Inc. Click here for terms of use.