ODE second order and Bessel function

Question

I have a function $xy''-y'+y=0$ that I'm trying to solve. I thought of solving it like this $ y''-y'/x+y/x=0 $ this you can write as $(y'/x)'+y=0 $ and then you can find the solution as a Bessel function. I got $y(x)=c_1x^1J_a(ax^b)+c_2x^1Y_a(ax^b)$ $a=2/3$ and $ b=3/2$

did I get it right?

Thanks Nachum

Answer 1

You can find the answer for example in http://eqworld.ipmnet.ru/en/solutions/ode/ode0206.pdf.