S[y] given by y = cosh æ + B sinhx, 0 0,
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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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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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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