Find a general solution to the linear homogenous differential equation of second order?

Question

R'' + (1/r)R' - λR = 0

where *R* is a function of *r*; find the general form of R(r)

Answer 1

The general solution to this differential equation is:

R(r) = C1(Bessel1(0,r√λ) + C2(1/√π)(Bessel2(0,r√λ)

where C1 and C2 are constants, and Bessel1 and Bessel2 are the Bessel functions of the first and second kind I(z) and K(z).