\[ y''(x)=-\frac {y(x) \left (4 a (a+1) x^4-2 a \left (x^2-1\right ) x^2+\left (x^2-1\right )^2 \left (x^2-v^2\right )\right )}{x^2 \left (x^2-1\right )^2}-\frac {\left ((1-4 a) x^2-1\right ) y'(x)}{x \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.784432 (sec), leaf count = 86
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{a+1} x^v \text {HeunC}\left [\frac {1}{4} (-2 a-4 v-3),\frac {1}{4},v+1,2,0,x^2\right ]+c_2 \left (x^2-1\right )^{a+1} x^{-v} \text {HeunC}\left [-\frac {a}{2}+v-\frac {3}{4},\frac {1}{4},1-v,2,0,x^2\right ]\right \}\right \}\] ✓ Maple : cpu = 2.627 (sec), leaf count = 58
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{a} \left ( {x}^{2}-1 \right ) \left ( {\it \_C1}\,{x}^{v}{\it HeunC} \left ( 0,v,1,{\frac {1}{4}},{\frac {a}{2}}+{\frac {1}{4}},{x}^{2} \right ) +{\it \_C2}\,{x}^{-v}{\it HeunC} \left ( 0,-v,1,{\frac {1}{4}},{\frac {a}{2}}+{\frac {1}{4}},{x}^{2} \right ) \right ) \right \} \]