\[ \boxed { x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 2\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -v \left ( v+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.023003 (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 = 0.078 (sec), leaf count = 51 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}(-v,-v;\,-2\,v;\,{x}^{-1})}{x}^{v}+{\it \_C2}\, {\mbox {$_2$F$_1$}(v+1,v+1;\,2+2\,v;\,{x}^{-1})}{x}^{-v-1} \right \} \]