\[ y''(x)=-\frac {y(x) \left (4 a (a+1) x^4-2 a \left (x^2-1\right ) x^2+\left (x^2-1\right )^2 \left (x^2-v^2\right )\right )}{x^2 \left (x^2-1\right )^2}-\frac {\left ((1-4 a) x^2-1\right ) y'(x)}{x \left (x^2-1\right )} \] ✗ Mathematica : cpu = 5.38436 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (\unicode {f817}^6+4 a^2 \unicode {f817}^4-v^2 \unicode {f817}^4+2 a \unicode {f817}^4-2 \unicode {f817}^4+2 v^2 \unicode {f817}^2+2 a \unicode {f817}^2+\unicode {f817}^2-v^2\right ) \unicode {f818}(\unicode {f817})+\left (-4 a \unicode {f817}^5+\unicode {f817}^5+4 a \unicode {f817}^3-2 \unicode {f817}^3+\unicode {f817}\right ) \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^6-2 \unicode {f817}^4+\unicode {f817}^2\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.688 (sec), leaf count = 58
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{a} \left ( {x}^{2}-1 \right ) \left ( {\it \_C1}\,{x}^{v}{\it HeunC} \left ( 0,v,1,{\frac {1}{4}},{\frac {1}{4}}+{\frac {a}{2}},{x}^{2} \right ) +{\it \_C2}\,{x}^{-v}{\it HeunC} \left ( 0,-v,1,{\frac {1}{4}},{\frac {1}{4}}+{\frac {a}{2}},{x}^{2} \right ) \right ) \right \} \]