\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( -{v}^{2}+{x}^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.057007 (sec), leaf count = 18 \[ \left \{\left \{y(x)\to c_1 J_v(x)+c_2 Y_v(x)\right \}\right \} \]
Maple: cpu = 0.0 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{v}\left (x\right )}+{ \it \_C2}\,{{\sl Y}_{v}\left (x\right )} \right \} \]