\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-1/2\,{\frac { \left ( 3\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-1 \right ) }}+1/4\,{\frac {v \left ( v+1 \right ) y \left ( x \right ) }{{x}^{2}}}=0} \]
Mathematica: cpu = 0.109014 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to c_1 i^{-v} x^{-v/2} \, _2F_1\left (\frac {1}{2},-v;\frac {1}{2}-v;x\right )+c_2 i^{v+1} x^{\frac {v+1}{2}} \, _2F_1\left (\frac {1}{2},v+1;v+\frac {3}{2};x\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {v}{2}}} {\mbox {$_2$F$_1$}({\frac {1}{2}},-v;\,{\frac {1}{2}}-v;\,x)}+{\it \_C2 }\,{x}^{{\frac {1}{2}}+{\frac {v}{2}}} {\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}}+v;\,x)} \right \} \]