\[ y''(x)=-\frac {y(x) \left (-a^2 \left (x^2-1\right )^2-m^2-n (n+1) \left (x^2-1\right )\right )}{\left (x^2-1\right )^2}-\frac {2 x y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.21957 (sec), leaf count = 113
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{m/2} \text {HeunC}\left [\frac {1}{4} \left (-a^2-m (m+1)+n^2+n\right ),-\frac {a^2}{4},\frac {1}{2},m+1,0,x^2\right ]+c_2 x \left (x^2-1\right )^{m/2} \text {HeunC}\left [\frac {1}{4} \left (-a^2-(m-n+1) (m+n+2)\right ),-\frac {a^2}{4},\frac {3}{2},m+1,0,x^2\right ]\right \}\right \}\] ✓ Maple : cpu = 1.312 (sec), leaf count = 84
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{{\frac {m}{2}}} \left ( {\it HeunC} \left ( 0,{\frac {1}{2}},m,-{\frac {{a}^{2}}{4}},{\frac {1}{4}}+{\frac {{a}^{2}}{4}}+{\frac {{m}^{2}}{4}}-{\frac {{n}^{2}}{4}}-{\frac {n}{4}},{x}^{2} \right ) {\it \_C2}\,x+{\it HeunC} \left ( 0,-{\frac {1}{2}},m,-{\frac {{a}^{2}}{4}},{\frac {1}{4}}+{\frac {{a}^{2}}{4}}+{\frac {{m}^{2}}{4}}-{\frac {{n}^{2}}{4}}-{\frac {n}{4}},{x}^{2} \right ) {\it \_C1} \right ) \right \} \]