Page 176 - Essentials of applied mathematics for scientists and engineers

book Mobk070 March 22, 2007 11:7

166 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS

1 (γ − β)e −αt + (α − γ )e −βt + (β − α)e −γ t
15
(p + α)(p + β)(p + γ ) (α − β)(β − γ )(γ − α)
1 e −βt − e −αt [1 − (β − α)t]
16
2
(p + α) (p + β) (β − α) 2
1 1
2 −αt
17 t e
(p + α) 3 2
1 t k−1 −αt
e
18
(p + α) k (k − 1)!
p αe −αt − βe −βt
19
(p + α)(p + β) α − β
p
20 (1 − αt)e −αt
(p + α) 2
p α(β − γ )e −αt + β(γ − α)e −βt + γ (α − β)e −γ t
21
(p + α)(p + β)(p + γ ) (α − β)(β − γ )(γ − α)
p [β − α(β − α)t]e −αt − βe −βt
22
2
(p + α) (p + β) (β − α) 2
p 1 −αt
23 t 1 − αt e
(p + α) 3 2
α
24 sin αt
2
p + α 2
p
25 cos αt
2
p + α 2
α
26 sinh αt
2
p − α 2
p
27 cosh αt
2
p − α 2
x −x /4αt
2
−qx
28 e e
2(παt )
3 1/2
e −qx α 1/2 −x /4αt
2
29 e
q π t
e −qx x
30 erfc
p 2(αt) 1/2
e −qx αt 1/2 −x /4αt x
2
31 2 e − xerfc
qp π 2(αt) 1/2
e −qx x 2 x t 1/2 2
32 t + erfc − x e −x /4αt
p 2 2α 2(αt) 1/2 απ
e −qx (γ − β)e −αt + (α − γ )e −βt + (β − α)e −γ t
33
p 1+n/2 (α − β)(β − γ )(γ − α)