\[ y''(x)=\frac {v (v+1) y(x)}{4 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.0763451 (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 = 0.624 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {v}{2}}}{\mbox {$_2$F$_1$}({\frac {1}{2}},-v;\,{\frac {1}{2}}-v;\,x)}+{\it \_C2}\,{x}^{{\frac {1}{2}}+{\frac {v}{2}}}{\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}}+v;\,x)} \right \} \]