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Show that the change of variables y = x/2u trans- forms the differential equation y"+(1-) -0 3 y 0 4x2 into the Bessel equation x?u" + xu' + (x2 - 1)u = 0 and thereby write the general solution to the given dif- ferential equation.

Show that the change of variables y = x/2u trans- forms the differential equation y"+(1-) -0 3 y 0 4x2 into the Bessel equation x?u" + xu' + (x2 - 1)u = 0 and thereby write the general solution to the given dif- ferential 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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Show that the change of variables y = x/2u trans- forms the differential equation y"+(1-) -0 3 y 0 4x2 into the Bessel equation x?u" + xu' + (x2 - 1)u = 0 and thereby write the general solution to the given dif- ferential equation.
Transcribed Image Text:Show that the change of variables y = x/2u trans- forms the differential equation y"+(1-) -0 3 y 0 4x2 into the Bessel equation x?u" + xu' + (x2 - 1)u = 0 and thereby write the general solution to the given dif- ferential equation.
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