\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,{x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -v \left ( v-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.021503 (sec), leaf count = 62 \[ \left \{\left \{y(x)\to c_1 e^{-x} \sqrt {x} J_{\frac {1}{2} (2 v-1)}(-i x)+c_2 e^{-x} \sqrt {x} Y_{\frac {1}{2} (2 v-1)}(-i x)\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}}\sqrt {x}{ {\sl I}_{v-{\frac {1}{2}}}\left (x\right )}+{\it \_C2}\,{{\rm e}^{-x}} \sqrt {x}{{\sl K}_{v-{\frac {1}{2}}}\left (x\right )} \right \} \]