S[y] given by y = cosh æ + B sinhx, 0 0,
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
100%
Deduce that there is only one stationary path.
(Note that a graphical argument alone is insufficien
you should give rigorous analysis to back up your explanation)
![S[y] = [”" dx (y¹² + y²),_y(0) = 1, y(v) = v, v > 0,
is given by
y = cosh æ + B sinh æ, 0 ≤ x ≤v,
where B and v are given by the solutions of the equations
v = cosh v + B sinh v and B² 1- 2 sinh v + 2B cosh v.
ƒ(v) = v² − 2v(1 + sinh v) cosh v + 1 + 2 sinh v.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2F12831a4b-4199-4af1-9d27-d0c3eb8b4fc7%2Fvgfh9zy_processed.png&w=3840&q=75)
Transcribed Image Text:S[y] = [”" dx (y¹² + y²),_y(0) = 1, y(v) = v, v > 0,
is given by
y = cosh æ + B sinh æ, 0 ≤ x ≤v,
where B and v are given by the solutions of the equations
v = cosh v + B sinh v and B² 1- 2 sinh v + 2B cosh v.
ƒ(v) = v² − 2v(1 + sinh v) cosh v + 1 + 2 sinh v.
-
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