\[ y''(x)=-\frac {\left (-(2 v+1)^2+x^2-1\right ) y(x)}{\left (x^2-1\right )^2}-\frac {\left (3 x^2-1\right ) y'(x)}{x \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.130549 (sec), leaf count = 72
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{-v-\frac {1}{2}} \, _2F_1\left (-v,-v;-2 v;1-x^2\right )+c_2 \left (x^2-1\right )^{v+\frac {1}{2}} \, _2F_1\left (v+1,v+1;2 v+2;1-x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.869 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{-{\frac {1}{2}}-v}{\mbox {$_2$F$_1$}(-v,-v;\,-2\,v;\,-{x}^{2}+1)}+{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{v+{\frac {1}{2}}}{\mbox {$_2$F$_1$}(v+1,v+1;\,2\,v+2;\,-{x}^{2}+1)} \right \} \]