\[ \left (x^2-1\right ) y''(x)-v (v+1) y(x)=0 \] ✓ Mathematica : cpu = 0.0809444 (sec), leaf count = 56
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (-\frac {v}{2}-\frac {1}{2},\frac {v}{2};\frac {1}{2};x^2\right )+i c_2 x \, _2F_1\left (-\frac {v}{2},\frac {v+1}{2};\frac {3}{2};x^2\right )\right \}\right \}\]
✓ Maple : cpu = 0.057 (sec), leaf count = 52
\[ \left \{ y \left ( x \right ) =- \left ( x-1 \right ) \left ( 1+x \right ) \left ( {\mbox {$_2$F$_1$}(1-{\frac {v}{2}},{\frac {3}{2}}+{\frac {v}{2}};\,{\frac {3}{2}};\,{x}^{2})}{\it \_C2}\,x+{\it \_C1}\,{\mbox {$_2$F$_1$}(1+{\frac {v}{2}},{\frac {1}{2}}-{\frac {v}{2}};\,{\frac {1}{2}};\,{x}^{2})} \right ) \right \} \]