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Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x + 2)y=0, 0 < x? Justify your answer.

Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x + 2)y=0, 0 < x? Justify your answer.

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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### Problem Statement Are \( y_1(x) = x \), \( y_2(x) = xe^x \) a fundamental set of solutions for the equation \[ x^2 y'' - x(x+2)y' + (x+2)y = 0, \, 0 < x ? \] Justify your answer.
Transcribed Image Text:### Problem Statement Are \( y_1(x) = x \), \( y_2(x) = xe^x \) a fundamental set of solutions for the equation \[ x^2 y'' - x(x+2)y' + (x+2)y = 0, \, 0 < x ? \] Justify your answer.
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