1550078481-Ordinary_Differential_Equations__Roberts_

Appendix C

Laplace Transforms

Function (Inverse Transform)

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

1

xn, n a positive integer

sin bx

cos bx

sinhbx

cosh bx

xneax, n a positive integer

eax sin bx

eax cos bx

eax sinhbx

eax coshbx

u(x - c), c 2: 0

o(x - c), c 2: 0

Transform

F(s) = L[f(x)] = f 0 ""' e-sx f(x) dx

1

s-a

1

s

n!

sn+l

b

s2 + b2

s

s2 + b2

b

s2 - b2

s

s2 - b2

n!

b

(s-a)^2 +b^2

s-a

(s - a)^2 + b^2

b

(s - a)^2 - b^2

s-a

(s - a)^2 - b^2

s

for s >a

for s > 0

for s > 0

for s > 0

for s > 0

for s > lbl

for s > lbl

for s >a

for s >a

for s >a

for s > lbl +a

for s > lbl +a

for s > 0

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