Consider the Sturm-Liouville eigenvalue problem on 0 ≤ x ≤ 2, y" + 2y = 0, y(0) = 0; y(2) = y'(2). 1. Assume the infinite set of eigenvalues are ordered so that do < ₁ < ₂ <.... Let p = [20] and give an implicit equation for p of the form p = f(p). P 2. Now let q = |2₁| and give an implicit equation for q of the form q = g(q). q= 3. Consider the eigenvalue nas n→ ∞. Determine that Ana(2n + 1)² in this limit, and give an equation for a. [HINT: it may help to think graphically in this limit] α =
Consider the Sturm-Liouville eigenvalue problem on 0 ≤ x ≤ 2, y" + 2y = 0, y(0) = 0; y(2) = y'(2). 1. Assume the infinite set of eigenvalues are ordered so that do < ₁ < ₂ <.... Let p = [20] and give an implicit equation for p of the form p = f(p). P 2. Now let q = |2₁| and give an implicit equation for q of the form q = g(q). q= 3. Consider the eigenvalue nas n→ ∞. Determine that Ana(2n + 1)² in this limit, and give an equation for a. [HINT: it may help to think graphically in this limit] α =
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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Dd.99.
![Consider the Sturm-Liouville eigenvalue problem on 0 ≤ x ≤ 2,
y" + 2y = 0,
y(0) = 0; y(2) = y'(2).
1. Assume the infinite set of eigenvalues are ordered so that do < ₁ <^₂ <.... Let p = [20] and give an implicit equation for p of the form p = f(p).
P
2. Now let q = ₁ and give an implicit equation for q of the form q = g(q).
q=
3. Consider the eigenvalue nas n→ ∞. Determine that n~ a(2n + 1)² in this limit, and give an equation for a. [HINT: it may help to think graphically
in this limit]
α =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe70c8743-1c47-4a3c-a696-b5ed8cd8e2f3%2F6f3c3b57-1cec-49f5-ac8c-02204b622d04%2Fuve5zxnj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the Sturm-Liouville eigenvalue problem on 0 ≤ x ≤ 2,
y" + 2y = 0,
y(0) = 0; y(2) = y'(2).
1. Assume the infinite set of eigenvalues are ordered so that do < ₁ <^₂ <.... Let p = [20] and give an implicit equation for p of the form p = f(p).
P
2. Now let q = ₁ and give an implicit equation for q of the form q = g(q).
q=
3. Consider the eigenvalue nas n→ ∞. Determine that n~ a(2n + 1)² in this limit, and give an equation for a. [HINT: it may help to think graphically
in this limit]
α =
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