\[ x (n-v-1) (n+v) y(x)-\left (2 (n-1) x^2+2 n-1\right ) y'(x)+x \left (x^2+1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.143067 (sec), leaf count = 87
\[\left \{\left \{y(x)\to c_2 x^{2 n} \, _2F_1\left (\frac {n}{2}-\frac {v}{2},\frac {n}{2}+\frac {v}{2}+\frac {1}{2};n+1;-x^2\right )+c_1 \, _2F_1\left (-\frac {n}{2}-\frac {v}{2},-\frac {n}{2}+\frac {v}{2}+\frac {1}{2};1-n;-x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.477 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={x}^{n} \left ( {\it LegendreQ} \left ( v,n,\sqrt {{x}^{2}+1} \right ) {\it \_C2}+{\it LegendreP} \left ( v,n,\sqrt {{x}^{2}+1} \right ) {\it \_C1} \right ) \right \} \]