\[ -v (v+1) y(x)+(x-1) x y''(x)+(2 x-1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0237699 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_1 P_v(2 x-1)+c_2 Q_v(2 x-1)\right \}\right \}\] ✓ Maple : cpu = 0.125 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-v,-v;\,-2\,v;\,{x}^{-1})}{x}^{v}+{\it \_C2}\,{\mbox {$_2$F$_1$}(v+1,v+1;\,2\,v+2;\,{x}^{-1})}{x}^{-v-1} \right \} \]