Prove that Define functions f(x) and g(x) as follows: 2 2 f(x) = 7/7 S e-tedt, g(x) = ²/1/²0 L {f(t)} g(8/2)²/4 8 ²dt 0-12

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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Prove that
Define functions f(x) and g(x) as follows:
2
f(x)
e-t² dt,
3 5.²
=
g(x)
g(s/2) ²/4
L {f(t)}
S
2
-t²
=
- 3 = 5.²" d².
dt
I
Transcribed Image Text:Prove that Define functions f(x) and g(x) as follows: 2 f(x) e-t² dt, 3 5.² = g(x) g(s/2) ²/4 L {f(t)} S 2 -t² = - 3 = 5.²" d². dt I
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