\[ y''(x)=-\frac {\left (-(2 v+1)^2+x^2-1\right ) y(x)}{\left (x^2-1\right )^2}-\frac {\left (3 x^2-1\right ) y'(x)}{x \left (x^2-1\right )} \] ✗ Mathematica : cpu = 1.42224 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817} \left (\unicode {f817}^2-4 v^2-4 v-2\right ) \unicode {f818}(\unicode {f817})+\left (3 \unicode {f817}^4-4 \unicode {f817}^2+1\right ) \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^5-2 \unicode {f817}^3+\unicode {f817}\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.375 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{-v-{\frac {1}{2}}}{\mbox {$_2$F$_1$}(-v,-v;\,-2\,v;\,-{x}^{2}+1)}+{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{v+{\frac {1}{2}}}{\mbox {$_2$F$_1$}(v+1,v+1;\,2\,v+2;\,-{x}^{2}+1)} \right \} \]