Obtain the general solution of each of the following equations in terms of Bessel functions: а.) ху" (х) — Зу (х) + ху (х) — 0 for x > 0, b.) xy" (x) + (2x + 1)y'(x) + (2x + 1)y(x) = 0 for x > 0, с.) y"(x) + x²y(x) = 0 %3D for -o 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Obtain the general solution of each of the following equations in terms of Bessel
functions:
а.)
xy"(x) – 3y'(x) + xy(x) = 0
for x > 0,
b.)
xy" (x) + (2x + 1)y'(x) + (2x + 1)y(x) = 0
for x > 0,
с.)
y"(x) +x²y(x) = 0
for -0 <x < +o,
d.)
xy" (x) + (2x + 1)y'(x) + y(x) = 0
for x > 0.
Transcribed Image Text:Obtain the general solution of each of the following equations in terms of Bessel functions: а.) xy"(x) – 3y'(x) + xy(x) = 0 for x > 0, b.) xy" (x) + (2x + 1)y'(x) + (2x + 1)y(x) = 0 for x > 0, с.) y"(x) +x²y(x) = 0 for -0 <x < +o, d.) xy" (x) + (2x + 1)y'(x) + y(x) = 0 for x > 0.
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