Deduce that there is only one stationary path.(Note that a graphical argument alone is insufficienyou should give rigorous analysis to back up your explanation) S[y] = [”" dx (y¹² + y²),_y(0) = 1, y(v) = v, v > 0,is given byy = cosh æ + B sinh æ, 0 ≤ x ≤v,where B and v are given by the solutions of the equationsv = 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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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.
-

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