Show that the eigenvalue problem 2²y"+ 2ry+ (32² + (2² +1³) v = 0₁ y = 0, y(-1)= y(1) = 0, with eigenvalue A, can be written as a constrained variational problem with functional S[y] = [² dx (x²y^² − 3x²y²) and constraint = [₁, dr. y² (1+x²)³ with boundary conditions y(-1) = y(1) = 0. C[y] =
Show that the eigenvalue problem 2²y"+ 2ry+ (32² + (2² +1³) v = 0₁ y = 0, y(-1)= y(1) = 0, with eigenvalue A, can be written as a constrained variational problem with functional S[y] = [² dx (x²y^² − 3x²y²) and constraint = [₁, dr. y² (1+x²)³ with boundary conditions y(-1) = y(1) = 0. C[y] =
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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![Show that the eigenvalue problem
2²y² + 2xy² + (3x² + (x² + 1jª) v =
y = 0, y(-1) = y(1) = 0,
with eigenvalue A, can be written as a constrained variational
problem with functional
S[y] = dz (x²y/² - 3x²y²)
[₁₁
and constraint
C[w] = [,d²₁ 222² =
dx
(1+x²)³
with boundary conditions
y(-1)= y(1) = 0.
1,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2F26974b0c-6b5f-401a-9390-2d949c2f47a1%2F1sc3apb_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the eigenvalue problem
2²y² + 2xy² + (3x² + (x² + 1jª) v =
y = 0, y(-1) = y(1) = 0,
with eigenvalue A, can be written as a constrained variational
problem with functional
S[y] = dz (x²y/² - 3x²y²)
[₁₁
and constraint
C[w] = [,d²₁ 222² =
dx
(1+x²)³
with boundary conditions
y(-1)= y(1) = 0.
1,
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