Solve this equation to show that the stationary path is a sin wr 262 y=a sinh (@(2 −1))+ßsinh(@(z−2)) . where α = B = 1 sinh. 1 sinhw 1+ a sin 2w 2w² b cosh w 2w b cosh 2w W a sin w 2w² + bx cosh wr 2w
Solve this equation to show that the stationary path is a sin wr 262 y=a sinh (@(2 −1))+ßsinh(@(z−2)) . where α = B = 1 sinh. 1 sinhw 1+ a sin 2w 2w² b cosh w 2w b cosh 2w W a sin w 2w² + bx cosh wr 2w
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 45E
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Question
![Solve this equation to show that the stationary path is
a sin wa
262
y=a sinh (@(z − 1)) +ßsinh(@(2 − 2))
-
where
α =
=
1
sinhw
1
sinh
1+
a sin 2w
26²
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%2Fc5301d05-9732-4305-8779-78d7f46d08b2%2F1vv66i_processed.png&w=3840&q=75)
Transcribed Image Text:Solve this equation to show that the stationary path is
a sin wa
262
y=a sinh (@(z − 1)) +ßsinh(@(2 − 2))
-
where
α =
=
1
sinhw
1
sinh
1+
a sin 2w
26²
b cosh w
2w
b cosh 2w
a sin w
262
W
]
+
bx cosh wx
2w
![Let a,
is
b and w be constants, with w‡0.
the
Euler-Lagrange equation for the functional
2
S[y] = [² da (y² + w²y² + 2y(a sin wa + b sinhwa)),
1
y(1) = 0, y(2) = 1,
y" - w²y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1.
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2Fc5301d05-9732-4305-8779-78d7f46d08b2%2Frijcnec_processed.png&w=3840&q=75)
Transcribed Image Text:Let a,
is
b and w be constants, with w‡0.
the
Euler-Lagrange equation for the functional
2
S[y] = [² da (y² + w²y² + 2y(a sin wa + b sinhwa)),
1
y(1) = 0, y(2) = 1,
y" - w²y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1.
2
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