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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
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?] =
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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