\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( 3\,{x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( {x}^{2}-1 \right ) }}-{\frac { \left ( {x}^{2}-1- \left ( 2\,v+1 \right ) ^{2} \right ) y \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 1.452684 (sec), leaf count = 88 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817} \left (\unicode {f817}^2-4 v^2-4 v-2\right ) \unicode {f818}(\unicode {f817})+\left (3 \unicode {f817}^4-4 \unicode {f817}^2+1\right ) \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^5-2 \unicode {f817}^3+\unicode {f817}\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \} \]
Maple: cpu = 0.124 (sec), leaf count = 69 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{- {\frac {1}{2}}-v}{\mbox {$_2$F$_1$}(-v,-v;\,-2\,v;\,-{x}^{2}+1)}+{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{v+{\frac {1}{2}}} {\mbox {$_2$F$_1$}(v+1,v+1;\,2+2\,v;\,-{x}^{2}+1)} \right \} \]