\[ \boxed { \left ( {x}^{2}+1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -v \left ( v-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.018502 (sec), leaf count = 30 \[ \left \{\left \{y(x)\to c_1 P_{v-1}(i x)+c_2 Q_{v-1}(i x)\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( v-1,ix \right ) +{\it \_C2}\,{\it LegendreQ} \left ( v-1,ix \right ) \right \} \]