Let y₁(x) and y₂(x) be any two twice differentiable functions, not necessarily eigenfunctions, in an interval a ≤x≤ b, then y₂L[y₁] - y₁L[y₂] = [p(x){y2y₁´— ¥1¥2'}]', where a prime denotes differentiation with respect to x, is called Lagrange's Identity.
Let y₁(x) and y₂(x) be any two twice differentiable functions, not necessarily eigenfunctions, in an interval a ≤x≤ b, then y₂L[y₁] - y₁L[y₂] = [p(x){y2y₁´— ¥1¥2'}]', where a prime denotes differentiation with respect to x, is called Lagrange's Identity.
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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![Let y₁(x) and y₂(x) be any two twice differentiable functions, not
necessarily eigenfunctions, in an interval a ≤x≤ b, then
y₂L[y₁] - y₁L[y₂] = [p(x) {y₂y₁'- Y₁Y2'}]',
where a prime denotes differentiation with respect to x, is called Lagrange's
Identity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14ecf344-ce8f-4775-bc92-58dda47891ff%2Fa6f63436-7374-4fb1-b76e-5ed0c7d0a3ce%2Fdzkcwsb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let y₁(x) and y₂(x) be any two twice differentiable functions, not
necessarily eigenfunctions, in an interval a ≤x≤ b, then
y₂L[y₁] - y₁L[y₂] = [p(x) {y₂y₁'- Y₁Y2'}]',
where a prime denotes differentiation with respect to x, is called Lagrange's
Identity.
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