Use the substitution Y(*)= x* · u(x }to convert the equation 2 d²y dy +ax- +(1+x°x* )y = 0 2..2 dx? dx
Use the substitution Y(*)= x* · u(x }to convert the equation 2 d²y dy +ax- +(1+x°x* )y = 0 2..2 dx? dx
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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Transcribed Image Text:Use the substitution y(x)= x* . u(x)to
convert the equation
d'y
dy
+ax-
dx?
dx
(1+ **x* ) y = 0
x?
in which ais a parameter, into an equation
for "(x).Find the values of a and Athat make
the equation in ux()Bessel's equation of
order zero. Use the result to find the general
их
solution yx() that corresponds to the value
of a.
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