(1) Recall the formula 2-* . r (s) (+ > 0, => 0). (*) t8-1 e=tz dt %3D Know that (*) is true also for s > 0, and (- >0, sus). = x e'y = x cos y + i ·x sin y · 0, 2 Rewrite the formula (*) accordingly. Answer - tx e - itx e-i sy .r (s) dt. t=0 || || -tz (cos y) cos (s y) – i sin (sy) cos (tx sin y) i sin (tr sin y) e (2) From (1), -t3(cos v) cos - tx ( cos y cos (sy) I (s) dt, e COS t=0 sin (sy) I (s) - tz (cos y) sin e dt.
(1) Recall the formula 2-* . r (s) (+ > 0, => 0). (*) t8-1 e=tz dt %3D Know that (*) is true also for s > 0, and (- >0, sus). = x e'y = x cos y + i ·x sin y · 0, 2 Rewrite the formula (*) accordingly. Answer - tx e - itx e-i sy .r (s) dt. t=0 || || -tz (cos y) cos (s y) – i sin (sy) cos (tx sin y) i sin (tr sin y) e (2) From (1), -t3(cos v) cos - tx ( cos y cos (sy) I (s) dt, e COS t=0 sin (sy) I (s) - tz (cos y) sin e dt.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(1) Recall the formula
2-* . r (s)
(+ > 0, => 0).
(*)
t8-1 e=tz dt
%3D
Know that (*) is true also for s > 0, and
(- >0, sus).
= x e'y =
x cos y + i ·x sin y
· 0,
2
Rewrite the formula (*) accordingly.
Answer
- tx
e
- itx
e-i sy .r (s)
dt.
t=0
||
||
-tz (cos y)
cos (s y) – i sin (sy)
cos (tx sin y)
i sin (tr sin y)
e
(2)
From (1),
-t3(cos v) cos
- tx ( cos y
cos (sy) I (s)
dt,
e
COS
t=0
sin (sy) I (s)
- tz (cos y)
sin
e
dt.
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