\[ (n-v-1) (n+v) y(x)-2 (n-1) x y'(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0176256 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{n/2} P_v^n(x)+c_2 \left (x^2-1\right )^{n/2} Q_v^n(x)\right \}\right \}\] ✓ Maple : cpu = 0.049 (sec), leaf count = 27
\[y \relax (x ) = \left (x^{2}-1\right )^{\frac {n}{2}} \left (\LegendreQ \left (v , n , x\right ) c_{2}+\LegendreP \left (v , n , x\right ) c_{1}\right )\]