\[ -v (v+1) y(x)+\left (x^2-1\right ) y''(x)+2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0126103 (sec), leaf count = 18
DSolve[-(v*(1 + v)*y[x]) + 2*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\{\{y(x)\to c_1 P_v(x)+c_2 Q_v(x)\}\}\] ✓ Maple : cpu = 0.035 (sec), leaf count = 15
dsolve((x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-v*(v+1)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \LegendreP \left (v , x\right )+c_{2} \LegendreQ \left (v , x\right )\]