3 Mathematica. Time used: 0.022 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+1/x*D[y[x],x]+k^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]

\begin{align*} y(x)&\to c_1 \operatorname {BesselJ}(0,k x)+c_2 \operatorname {BesselY}(0,k x) \end{align*}