Show that y = x!/2 w(x²) is a solution of the differential equation y" + 4x?y = 0, x > 0, whenever w is a solution of Bessel's equation of order that is t?w" + tw' + (t² -) w = 0, t> 0 %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Show that y = x'/2 w(x²) is a solution of the differential equation y" + 4x²y = 0, x > 0,
whenever w is a solution of Bessel's equation of order that is
t?w" + tw' + (t² -)w = 0, t> 0
(Hint: After differentiating, substituting, and simplifying, then let t = x²)
16.
Transcribed Image Text:2. Show that y = x'/2 w(x²) is a solution of the differential equation y" + 4x²y = 0, x > 0, whenever w is a solution of Bessel's equation of order that is t?w" + tw' + (t² -)w = 0, t> 0 (Hint: After differentiating, substituting, and simplifying, then let t = x²) 16.
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