\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac {x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}-1}}-{\frac { \left ( -{a}^{2} \left ( {x}^{2}-1 \right ) ^{2}-n \left ( n+1 \right ) \left ( {x}^{2}-1 \right ) -{m}^{2} \right ) y \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 2.321295 (sec), leaf count = 104 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (-a^2 \unicode {f817}^4+2 a^2 \unicode {f817}^2-n^2 \unicode {f817}^2-n \unicode {f817}^2-a^2-m^2+n^2+n\right ) \unicode {f818}(\unicode {f817})+\left (2 \unicode {f817}^3-2 \unicode {f817}\right ) \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^4-2 \unicode {f817}^2+1\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 92 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{{ \frac {m}{2}}}{\it HeunC} \left ( 0,-{\frac {1}{2}},m,-{\frac {{a}^{2} }{4}},{\frac {1}{4}}+{\frac {{a}^{2}}{4}}+{\frac {{m}^{2}}{4}}-{\frac {{n}^{2}}{4}}-{\frac {n}{4}},{x}^{2} \right ) +{\it \_C2}\, \left ( {x}^ {2}-1 \right ) ^{{\frac {m}{2}}}x{\it HeunC} \left ( 0,{\frac {1}{2}},m, -{\frac {{a}^{2}}{4}},{\frac {1}{4}}+{\frac {{a}^{2}}{4}}+{\frac {{m}^ {2}}{4}}-{\frac {{n}^{2}}{4}}-{\frac {n}{4}},{x}^{2} \right ) \right \} \]