Solve this equation to show that the stationary path is x(1+2A) (3 + 2A) 1 + 2 y(x) = = X
Solve this equation to show that the stationary path is x(1+2A) (3 + 2A) 1 + 2 y(x) = = X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Consider the functional
2
S[(y)] = [₁² dx ln(1 + x²y'), y(1) = 0, y(2) = A,
where A is a constant and y is a continuously differentiable function for
1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2,
and let e be a constant. Let A = S[y+ ch] — S[y].
2
= cf ₁²
A = E
dx
y(x)
x²h' €²
=
x4h2
(1+x²y')²
1
& ff d
2
+0(€³).
if h(1) = h(2) = 0, then the term O(e) in this expansion
vanishes if y'(x) satisfies the equation
1 + x²y'
dx
dy
1 1
dx с x²
where c is a nonzero constant.
Solve this equation to show that the stationary path is
x(1+2A) − (3+2A) 1
+
2
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2Fde40ff23-22ef-44b6-893d-ac5cfa1f7cee%2F09zuj7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the functional
2
S[(y)] = [₁² dx ln(1 + x²y'), y(1) = 0, y(2) = A,
where A is a constant and y is a continuously differentiable function for
1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2,
and let e be a constant. Let A = S[y+ ch] — S[y].
2
= cf ₁²
A = E
dx
y(x)
x²h' €²
=
x4h2
(1+x²y')²
1
& ff d
2
+0(€³).
if h(1) = h(2) = 0, then the term O(e) in this expansion
vanishes if y'(x) satisfies the equation
1 + x²y'
dx
dy
1 1
dx с x²
where c is a nonzero constant.
Solve this equation to show that the stationary path is
x(1+2A) − (3+2A) 1
+
2
X
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
