Show that xvJv(x) satisfies the equation

Chapter 8, Problem 21E

(choose chapter or problem)

Show that $x^{v} J_{v}(x)$ satisfies the equation

$x y^{\prime \prime}+(1-2 v) y^{\prime}+x y=0, \quad x>0$

and use this result to find a solution for the equation

$x y^{\prime \prime}-2 y^{\prime}+x y=0, \quad x>0$

Equation Transcription:

${x}^{v}{J}_{v}(x)$

$xy''+(1-2v)y'+xy=0,\ \ \ x>0$

$xy''-2y'+xy=0$

Text Transcription

x^vJv(x)

xy''+(1-2v)y'+xy=0, x>0

xy''-2y'+xy=0

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