\[ y''(x)=\frac {v (v+1) y(x)}{x^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0663703 (sec), leaf count = 68
\[\left \{\left \{y(x)\to c_1 i^{-v} x^{-v} \, _2F_1\left (\frac {1}{2},-v;\frac {1}{2}-v;x^2\right )+c_2 i^{v+1} x^{v+1} \, _2F_1\left (\frac {1}{2},v+1;v+\frac {3}{2};x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.064 (sec), leaf count = 47
\[y \relax (x ) = c_{1} \hypergeom \left (\left [\frac {1}{2}, -v \right ], \left [\frac {1}{2}-v \right ], x^{2}\right ) x^{-v}+c_{2} \hypergeom \left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}+v \right ], x^{2}\right ) x^{v +1}\]