\[ (1-v) (v+2) y(x)+\left (x^2-1\right ) y''(x)-2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0113988 (sec), leaf count = 30
DSolve[(1 - v)*(2 + v)*y[x] - 2*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right ) P_v^2(x)+c_2 \left (x^2-1\right ) Q_v^2(x)\right \}\right \}\] ✓ Maple : cpu = 0.044 (sec), leaf count = 24
dsolve((x^2-1)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-(v+2)*(v-1)*y(x)=0,y(x))
\[y \left (x \right ) = \left (x -1\right ) \left (1+x \right ) \left (c_{2} \LegendreQ \left (v , 2, x\right )+c_{1} \LegendreP \left (v , 2, x\right )\right )\]