\[ -2 (v-1) x y'(x)-2 v y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0142028 (sec), leaf count = 42
DSolve[-2*v*y[x] - 2*(-1 + v)*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{v/2} P_v^v(x)+c_2 \left (x^2-1\right )^{v/2} Q_v^v(x)\right \}\right \}\] ✓ Maple : cpu = 0.125 (sec), leaf count = 28
dsolve((x^2-1)*diff(diff(y(x),x),x)-2*(v-1)*x*diff(y(x),x)-2*v*y(x)=0,y(x))
\[y \left (x \right ) = \left (x^{2}-1\right )^{v} \left (\hypergeom \left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}\right ], x^{2}\right ) c_{2} x +c_{1}\right )\]