\[ x (n-v-1) (n+v) y(x)-\left (2 (n-1) x^2+2 n-1\right ) y'(x)+x \left (x^2+1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.197329 (sec), leaf count = 75
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {1}{2} (-n-v),\frac {1}{2} (-n+v+1);1-n;-x^2\right )+c_2 x^{2 n} \, _2F_1\left (\frac {n-v}{2},\frac {1}{2} (n+v+1);n+1;-x^2\right )\right \}\right \}\]
✓ Maple : cpu = 0.197 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={x}^{n} \left ( {\it LegendreQ} \left ( v,n,\sqrt {{x}^{2}+1} \right ) {\it \_C2}+{\it LegendreP} \left ( v,n,\sqrt {{x}^{2}+1} \right ) {\it \_C1} \right ) \right \} \]