\[ -v (v+1) y(x)+(x-1) x y''(x)+(2 x-1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0184036 (sec), leaf count = 26
\[\{\{y(x)\to c_1 P_v(2 x-1)+c_2 Q_v(2 x-1)\}\}\] ✓ Maple : cpu = 0.258 (sec), leaf count = 51
\[\left \{y \left (x \right ) = c_{1} x^{v} \hypergeom \left (\left [-v , -v \right ], \left [-2 v \right ], \frac {1}{x}\right )+c_{2} x^{-v -1} \hypergeom \left (\left [v +1, v +1\right ], \left [2 v +2\right ], \frac {1}{x}\right )\right \}\]