\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( \left ( 1-4\,a \right ) {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( {x}^{2}-1 \right ) }}-{\frac { \left ( \left ( -{v}^{2}+{x}^{2} \right ) \left ( {x}^{2}-1 \right ) ^{2}+4\,a \left ( a+1 \right ) {x}^{4}-2\,a{x}^{2} \left ( {x}^{2}-1 \right ) \right ) y \left ( x \right ) }{{x}^{2} \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 4.464067 (sec), leaf count = 127 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (\unicode {f817}^6+4 a^2 \unicode {f817}^4-v^2 \unicode {f817}^4+2 a \unicode {f817}^4-2 \unicode {f817}^4+2 v^2 \unicode {f817}^2+2 a \unicode {f817}^2+\unicode {f817}^2-v^2\right ) \unicode {f818}(\unicode {f817})+\left (-4 a \unicode {f817}^5+\unicode {f817}^5+4 a \unicode {f817}^3-2 \unicode {f817}^3+\unicode {f817}\right ) \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^6-2 \unicode {f817}^4+\unicode {f817}^2\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 69 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{v} \left ( {x}^{2}-1 \right ) ^{a} \left ( {x}^{2}-1 \right ) {\it HeunC} \left ( 0,v,1,{ \frac {1}{4}},{\frac {a}{2}}+{\frac {1}{4}},{x}^{2} \right ) +{\it \_C2 }\,{x}^{-v} \left ( {x}^{2}-1 \right ) ^{a} \left ( {x}^{2}-1 \right ) { \it HeunC} \left ( 0,-v,1,{\frac {1}{4}},{\frac {a}{2}}+{\frac {1}{4}}, {x}^{2} \right ) \right \} \]