6. Find a series solution in powers of x of the IVP y" + λxy = 0, y(0) = 1, y'(0) = 0, where λ is a given positive parameter. Approximating the solution by the Taylor polynomial of degree 6, find (approximately) the minimal number L > 0 such that A is an eigenvalue of the BVP y" + λxy = 0, y'(0)=0, _y(L) = 0.
6. Find a series solution in powers of x of the IVP y" + λxy = 0, y(0) = 1, y'(0) = 0, where λ is a given positive parameter. Approximating the solution by the Taylor polynomial of degree 6, find (approximately) the minimal number L > 0 such that A is an eigenvalue of the BVP y" + λxy = 0, y'(0)=0, _y(L) = 0.
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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![6. Find a series solution in powers of x of the IVP
y" + λxy = 0,
where A is a given positive parameter. Approximating the solution by the Taylor
polynomial of degree 6, find (approximately) the minimal number L > 0 such that
A is an eigenvalue of the BVP
y(0) = 1, y'(0) = 0,
y" + λxy = 0,
y'(0)
0, y(L) = 0.
[Interpretation: when will a uniform vertical column buckle under its own weight?]
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd104ea5e-59f4-47a3-a0d3-8c9f1ad3b57c%2Fd51ca44f-5a4d-446b-b38d-12064cb2d7bf%2F9b4mtk_processed.png&w=3840&q=75)
Transcribed Image Text:6. Find a series solution in powers of x of the IVP
y" + λxy = 0,
where A is a given positive parameter. Approximating the solution by the Taylor
polynomial of degree 6, find (approximately) the minimal number L > 0 such that
A is an eigenvalue of the BVP
y(0) = 1, y'(0) = 0,
y" + λxy = 0,
y'(0)
0, y(L) = 0.
[Interpretation: when will a uniform vertical column buckle under its own weight?]
=
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