Show that the equation and boundary conditions d dx 22 dy dx + Axy = 0, y(1) = 0, y'(2) = 0, form a regular Sturm-Liouville system. Show further that the system can be written as a constrained variational problem with functional -2 S[y] = [² dx x²y², and constraint dx x2 y2, y(1) = 0, C[y] = [² dx xy² = 1.
Show that the equation and boundary conditions d dx 22 dy dx + Axy = 0, y(1) = 0, y'(2) = 0, form a regular Sturm-Liouville system. Show further that the system can be written as a constrained variational problem with functional -2 S[y] = [² dx x²y², and constraint dx x2 y2, y(1) = 0, C[y] = [² dx xy² = 1.
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 equation and boundary conditions
d
dx
22
dy
dx
+ Axy = 0, y(1) = 0, y'(2) = 0,
form a regular Sturm-Liouville system.
Show further that the system can be written as a constrained
variational problem with functional
-2
S[y] = [² dx x²y²,
and constraint
dx x2 y2, y(1) = 0,
C[y] = [² dx xy² = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2F74546993-d293-4138-ae99-cbf5fed2a820%2Fhcv152_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the equation and boundary conditions
d
dx
22
dy
dx
+ Axy = 0, y(1) = 0, y'(2) = 0,
form a regular Sturm-Liouville system.
Show further that the system can be written as a constrained
variational problem with functional
-2
S[y] = [² dx x²y²,
and constraint
dx x2 y2, y(1) = 0,
C[y] = [² dx xy² = 1.
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