\[ y''(x)=-\frac {v (v+1) y(x)}{x^2 \left (x^2-1\right )}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0883112 (sec), leaf count = 86
\[\left \{\left \{y(x)\to c_1 i^{-v} x^{-v} \, _2F_1\left (\frac {1}{2}-\frac {v}{2},-\frac {v}{2};\frac {1}{2}-v;x^2\right )+c_2 i^{v+1} x^{v+1} \, _2F_1\left (\frac {v}{2}+\frac {1}{2},\frac {v}{2}+1;v+\frac {3}{2};x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.148 (sec), leaf count = 57
\[\left \{y \left (x \right ) = c_{1} x^{-v} \hypergeom \left (\left [-\frac {v}{2}, -\frac {v}{2}+\frac {1}{2}\right ], \left [-v +\frac {1}{2}\right ], x^{2}\right )+c_{2} x^{v +1} \hypergeom \left (\left [\frac {v}{2}+1, \frac {v}{2}+\frac {1}{2}\right ], \left [v +\frac {3}{2}\right ], x^{2}\right )\right \}\]