1550078481-Ordinary_Differential_Equations__Roberts_

The Laplace Trans! orm Method 235

Table 5 .1 Laplace transforms and inverse Laplace t r ansforms

f(x) = .c-^1 (F(s)) F(s) = .C[f(x)]

eax --^1 for 8>a

s-a

1

1 - for s>O

8

xn ) --n! for s>O

8 n+l

n a posit ive integer

sin bx

b

--- for s>O

32 + b2

cos bx

s

for s>O

32 + b2

sinhbx

b

--- for s > lbl

32 - b2

coshbx

8

--- for s > lbl

32 - b2

xneax, n!

(s - a)n+l

for s>a

n a positive integer

eax sin bx

b

(s- a)^2 +b^2

for 3>a

eax cos bx

s - a

for

(s- a)^2 +b^2

s>a

eax sinhbx

b

for 8 > lbl +a

(s - a)^2 - b^2

eax cosh bx

s-a

for s > lbl +a

(8 - a)^2 - b^2