\[ y''(x)=\frac {v (v+1) y(x)}{4 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.0939401 (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 = 0.122 (sec), leaf count = 45
\[\left \{y \left (x \right ) = c_{1} x^{-\frac {v}{2}} \hypergeom \left (\left [\frac {1}{2}, -v \right ], \left [-v +\frac {1}{2}\right ], x\right )+c_{2} x^{\frac {v}{2}+\frac {1}{2}} \hypergeom \left (\left [\frac {1}{2}, v +1\right ], \left [v +\frac {3}{2}\right ], x\right )\right \}\]