y be a real constant with y² 1 for the parametric functional S[x, y)] = ['ª dt [√લ + 2y àý + y² – X(xÿ−ày)], λ>0, – with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. ds dx dy +7 = ds dx = 2(cy) and y ds 33 dy = 2(d+λx), where c and d are constants and
y be a real constant with y² 1 for the parametric functional S[x, y)] = ['ª dt [√લ + 2y àý + y² – X(xÿ−ày)], λ>0, – with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. ds dx dy +7 = ds dx = 2(cy) and y ds 33 dy = 2(d+λx), where c and d are constants and
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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Show that the stationary paths of this parametric functional.
![y be a real constant with y² 1 for the parametric functional
S[x, 3] = [ª dt [√ä² + 2y àÿ + ÿj² – A(xÿ — ày)],
-
-
> > 0,
with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
dx
ds
dy
+7 =
ds
dx dy
= 2(c->y) and y + =
ds ds
2(d+λx),
where c and d are constants and
s(t) = √¸² dt √ž² + 2y àÿ + ÿj².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2F62e388bb-cadf-419f-a174-abae69a61fc6%2Fryjocl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:y be a real constant with y² 1 for the parametric functional
S[x, 3] = [ª dt [√ä² + 2y àÿ + ÿj² – A(xÿ — ày)],
-
-
> > 0,
with the boundary conditions x(0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
dx
ds
dy
+7 =
ds
dx dy
= 2(c->y) and y + =
ds ds
2(d+λx),
where c and d are constants and
s(t) = √¸² dt √ž² + 2y àÿ + ÿj².
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