\[ y''(x)=\frac {2 x y'(x)}{x^2-1}-\frac {y(x) \left (\left (x^2-1\right ) x^2 (a-n) (a+n+1)+2 a x^2+n (n+1) \left (x^2-1\right )\right )}{x^2 \left (x^2-1\right )} \] ✗ Mathematica : cpu = 10.3707 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-2 \unicode {f818}'(\unicode {f817}) \unicode {f817}^3+\left (a^2 \unicode {f817}^4-n^2 \unicode {f817}^4+a \unicode {f817}^4-n \unicode {f817}^4-a^2 \unicode {f817}^2+2 n^2 \unicode {f817}^2+a \unicode {f817}^2+2 n \unicode {f817}^2-n^2-n\right ) \unicode {f818}(\unicode {f817})+\left (\unicode {f817}^4-\unicode {f817}^2\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 2.184 (sec), leaf count = 109
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunC} \left ( 0,-n-{\frac {1}{2}},-2,-{\frac {{a}^{2}}{4}}+{\frac {{n}^{2}}{4}}-{\frac {a}{4}}+{\frac {n}{4}},-{\frac {{n}^{2}}{4}}-{\frac {n}{4}}+{\frac {3}{4}}+{\frac {{a}^{2}}{4}}-{\frac {a}{4}},{x}^{2} \right ) {x}^{-n}+{\it \_C2}\,{\it HeunC} \left ( 0,n+{\frac {1}{2}},-2,-{\frac {{a}^{2}}{4}}+{\frac {{n}^{2}}{4}}-{\frac {a}{4}}+{\frac {n}{4}},-{\frac {{n}^{2}}{4}}-{\frac {n}{4}}+{\frac {3}{4}}+{\frac {{a}^{2}}{4}}-{\frac {a}{4}},{x}^{2} \right ) {x}^{n+1} \right \} \]