\[ x (n-v) (n+v+1) y(x)+\left (2 (n+1) x^2+2 n+1\right ) y'(x)+x \left (x^2+1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.149839 (sec), leaf count = 87
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {n}{2}-\frac {v}{2},\frac {n}{2}+\frac {v}{2}+\frac {1}{2};n+1;-x^2\right )+c_2 x^{-2 n} \, _2F_1\left (-\frac {n}{2}-\frac {v}{2},-\frac {n}{2}+\frac {v}{2}+\frac {1}{2};1-n;-x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.078 (sec), leaf count = 35
\[y \relax (x ) = x^{-n} \left (\LegendreQ \left (v , n , \sqrt {x^{2}+1}\right ) c_{2}+\LegendreP \left (v , n , \sqrt {x^{2}+1}\right ) c_{1}\right )\]