1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

ANSWERS 623

Section 12.8. Multiplication and D ivis io n b y t: page 561

1. [, (te-2t) = (s.1 2 )2.

3. .C (tsin3t) = (• 2 6.;. 9 )"

5. .C ( t sinh t) = (• 2 ~ 1 )2.

7. 
   

   .c(";^1 ) =ln.~ 1.

   
   


8. 
   

   .C (t sinbt) = t/_:g,)2.

   
   

ll. .c- 1 (tn (:~1}•) = 2 (e'~cost)_

1 3. y(t ) = te- t + t^2 e-t.

15. y(t) = Ctet.

17. y(t) = Ct.

1 9. y(t) = 1 - t.

Sect ion 12.9. I n verting the Laplace Transform: page 570

1. .c-^1 <.(:!h) = - 1 + 3e^1.

(^3) · .c-1( •(•+2)(4.2-6ss-- 12) 2) = 3 + 2e - 2t _ e2t ·
(^5) • .c-1( (s2• 2t2)(s+s±3 -1) 2 ) = e-2t + e' + 2te' ·

7. .c -^1 ( , 2 ~ 4 ) = ~sin 2t.

9. .c -^1 (•

3

+\' -•+^3 ) = - 3 + e' + e-^1 +cost +sint = - 3 + 2 cosh t + cost+ sint.

$ -·

11. .c-1(•

3

+~:~~-+^1 ) = - 1 + e^1 + e-^1 - cost + sin t = - 1 + 2cosh t - cost+sint.

3 .c- 1(•

(^3) +2s (^2) r.4•+2 ) t. 2t

1. (s2+l)s2+4) =COS +Sill.

1 5. y(t) = e-t + e- t sin 2t.

1 7. y(t ) = e-^1 +cos 2t + sin 2t.

19. y(t) = 1 + t.

21. x(t) = 2e -^21 - e^1 , and y(t ) = e -^2 t - 2e^1.