y be a real constant with √² 1 for the parametric functional S[x, y] = [" - dt +2√ àÿ †ÿ² − \(xÿ − xy)], >>0, - with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. Show the stationary paths of x & y as are below, ds しゅ噐 dy = 2(cy) and y where c and d are constants and s(t) [*²dt √² = [[* åt √ ž² + 2y bý + y². dx dy + ds ds = 2(d+\x), }
y be a real constant with √² 1 for the parametric functional S[x, y] = [" - dt +2√ àÿ †ÿ² − \(xÿ − xy)], >>0, - with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. Show the stationary paths of x & y as are below, ds しゅ噐 dy = 2(cy) and y where c and d are constants and s(t) [*²dt √² = [[* åt √ ž² + 2y bý + y². dx dy + ds ds = 2(d+\x), }
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![y be a real constant with √² 1 for the parametric functional
S[x, y]
=
["
-
dt +2√ àÿ †ÿ² − \(xÿ − xy)], >>0,
-
with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
Show the stationary paths of x & y as are below,
ds
しゅ噐
dy
=
2(cy) and y
where c and d are constants and
s(t) [*²dt √²
= [[* åt √ ž² + 2y bý + y².
dx dy
+
ds ds
=
2(d+\x),
}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2Ffcd84e6f-05e6-44c3-a607-0e8984a828d7%2F5vjr8sk_processed.png&w=3840&q=75)
Transcribed Image Text:y be a real constant with √² 1 for the parametric functional
S[x, y]
=
["
-
dt +2√ àÿ †ÿ² − \(xÿ − xy)], >>0,
-
with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
Show the stationary paths of x & y as are below,
ds
しゅ噐
dy
=
2(cy) and y
where c and d are constants and
s(t) [*²dt √²
= [[* åt √ ž² + 2y bý + y².
dx dy
+
ds ds
=
2(d+\x),
}
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