\[ \left (x^2-1\right ) y''(x)-v (v+1) y(x)=0 \] ✓ Mathematica : cpu = 0.0674738 (sec), leaf count = 58
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (-\frac {v}{2}-\frac {1}{2},\frac {v}{2};\frac {1}{2};x^2\right )+i c_2 x \, _2F_1\left (\frac {v}{2}+\frac {1}{2},-\frac {v}{2};\frac {3}{2};x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.19 (sec), leaf count = 52
\[\left \{y \left (x \right ) = -\left (x -1\right ) \left (x +1\right ) \left (c_{2} x \hypergeom \left (\left [-\frac {v}{2}+1, \frac {v}{2}+\frac {3}{2}\right ], \left [\frac {3}{2}\right ], x^{2}\right )+c_{1} \hypergeom \left (\left [\frac {v}{2}+1, -\frac {v}{2}+\frac {1}{2}\right ], \left [\frac {1}{2}\right ], x^{2}\right )\right )\right \}\]