Determine whether S[y] has a maximum or a minimum on this stationary path, and whether it is global or local.
Determine whether S[y] has a maximum or a minimum on this stationary path, and whether it is global or local.
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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Question
Determine whether S[y] has a maximum or a minimum on this stationary path, and whether it is global or local.
![Let a, b and w be constants, with w‡ 0.
is
S[y] =
y(1) = 0, y(2) = 1,
y" - w²y = a sin x +bsinh x, y(1)=0, g(2) = 1.
this equation to show that the stationary path is
a sin wx
2w²
Y
where
the Euler-Lagrange equation for the functional
[² dx (y¹² +w²y² + 2y (a sin wx + b sinh wx)),
α=
В
=
a sinh (@( − 1))+ßsinh(w(x – 2))
-
1
sinhw
1
sinhw
1+
a sin 2w
2w²
[b cosh w
2w
b cosh 2w
a sin w
26²
W
+
bx cosh wx
2w](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2F5a088830-db84-4f83-9fa5-9f7d62996de5%2F1wyplhe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a, b and w be constants, with w‡ 0.
is
S[y] =
y(1) = 0, y(2) = 1,
y" - w²y = a sin x +bsinh x, y(1)=0, g(2) = 1.
this equation to show that the stationary path is
a sin wx
2w²
Y
where
the Euler-Lagrange equation for the functional
[² dx (y¹² +w²y² + 2y (a sin wx + b sinh wx)),
α=
В
=
a sinh (@( − 1))+ßsinh(w(x – 2))
-
1
sinhw
1
sinhw
1+
a sin 2w
2w²
[b cosh w
2w
b cosh 2w
a sin w
26²
W
+
bx cosh wx
2w
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