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17. x²y" + xy' + (x² -v²)y=0 (Bessel equation)

17. x²y" + xy' + (x² -v²)y=0 (Bessel equation)

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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For Question 17: Find all singular points of the given
equation and determine whether each one is regular or irregular.

17. x²y" + xy' + (x²-v²)y=0 (Bessel equation) 18. (x+2)²(x - 1) y" + 3(x − 1) y' - 2(x + 2) y = 0 19. x(3x) y" +(x + 1) y' - 2y = 0 20. xy" +ey' + (3 cos x) y = 0 21. y" + (ln [x]) y' + 3xy = 0 22. (sin x)y" + xy' +4y=0 23. (x sin x) y" + 3y' + xy = 0
Transcribed Image Text:17. x²y" + xy' + (x²-v²)y=0 (Bessel equation) 18. (x+2)²(x - 1) y" + 3(x − 1) y' - 2(x + 2) y = 0 19. x(3x) y" +(x + 1) y' - 2y = 0 20. xy" +ey' + (3 cos x) y = 0 21. y" + (ln [x]) y' + 3xy = 0 22. (sin x)y" + xy' +4y=0 23. (x sin x) y" + 3y' + xy = 0
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