S[y] = [ "_ dx (y^² + y²), _y(0) = 1, y(v) = v, v > 0, is given by y = coshæ + B sinh x, 0 < * Συ, where B and v are given by the solutions of the equations v=cosh v+ B sinh v and B² 12 sinh v + 2B cosh v. Use these equations to show that v is given by the real solution(s) of ƒ(v) = 0, where f(v) = v² − 2v(1 + sinh v) cosh v + 1 + 2 sinh v.
S[y] = [ "_ dx (y^² + y²), _y(0) = 1, y(v) = v, v > 0, is given by y = coshæ + B sinh x, 0 < * Συ, where B and v are given by the solutions of the equations v=cosh v+ B sinh v and B² 12 sinh v + 2B cosh v. Use these equations to show that v is given by the real solution(s) of ƒ(v) = 0, where f(v) = v² − 2v(1 + sinh v) cosh v + 1 + 2 sinh v.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![S[y] = da
So dx (y'² + y²), y(0) = 1, y(v) = v, v > 0,
is given by
y = coshæ+Bsinhæ, 0≤su,
x
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.
Use these equations to show that v is given by the real solution(s) of
f(v) = 0, where
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%2F19aeb179-aafd-4874-b054-ee3b563293c5%2Fdrs9ofs_processed.png&w=3840&q=75)
Transcribed Image Text:S[y] = da
So dx (y'² + y²), y(0) = 1, y(v) = v, v > 0,
is given by
y = coshæ+Bsinhæ, 0≤su,
x
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.
Use these equations to show that v is given by the real solution(s) of
f(v) = 0, where
ƒ(v) = v² − 2v(1 + sinh v) cosh v + 1 + 2 sinh v.
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