\[ -(v-1) v y(x)+\left (x^2+1\right ) y''(x)+2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0247248 (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 = 0.095 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( v-1,ix \right ) +{\it \_C2}\,{\it LegendreQ} \left ( v-1,ix \right ) \right \} \]