Page 76 - LAPLACE TRANSFORM

4.0 DIFFERENTIAL EQUATION METHOD

4.1 SOLVE DIFFERENTIAL EQUATIONS USING LAPLACE

TRANSFORM

The Laplace transform is a powerful integral transform used to switch a function from
the time domain to the s-domain. The Laplace transform can be used in some cases
to solve linear differential equations with given initial conditions.

4.1.1 Table of Laplace Transform

First consider the following property of the Laplace transform:

Table of Laplace Transform

F(s) F(t), t> 0

First Derivative
sY (s ) − ) 0 ( y dy
y ( t),
'
dt
Second Derivative
s 2 Y ) (s − sy ) 0 ( − ' ) 0 ( y y ' ' (t ), d 2 y

dt 2

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