\[ -v (v+1) y(x)+(x-1) x y''(x)+(2 x-1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0172269 (sec), leaf count = 26
\[\{\{y(x)\to c_1 P_v(2 x-1)+c_2 Q_v(2 x-1)\}\}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 51
\[y \relax (x ) = c_{1} \hypergeom \left (\left [-v , -v \right ], \left [-2 v \right ], \frac {1}{x}\right ) x^{v}+c_{2} \hypergeom \left (\left [v +1, v +1\right ], \left [2 v +2\right ], \frac {1}{x}\right ) x^{-v -1}\]