\[ a \left (y(x)^2-2 x y(x)+1\right )+\left (x^2-1\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.241046 (sec), leaf count = 158
\[\left \{\left \{y(x)\to \frac {\left (x^2-1\right ) \left (c_1 \left (a x \left (x^2-1\right )^{\frac {a}{2}-1} P_{a-1}(x)+\left (x^2-1\right )^{\frac {a}{2}-1} (a P_a(x)-a x P_{a-1}(x))\right )+a x \left (x^2-1\right )^{\frac {a}{2}-1} Q_{a-1}(x)+\left (x^2-1\right )^{\frac {a}{2}-1} (a Q_a(x)-a x Q_{a-1}(x))\right )}{a \left (\left (x^2-1\right )^{a/2} Q_{a-1}(x)+c_1 \left (x^2-1\right )^{a/2} P_{a-1}(x)\right )}\right \}\right \}\] ✓ Maple : cpu = 0.252 (sec), leaf count = 231
\[\left \{y \left (x \right ) = \frac {-\left (x +1\right ) a \left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \HeunC \left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )+8 c_{1} \left (-\frac {a}{2}+\left (a -\frac {1}{2}\right ) x +\frac {1}{2}\right ) \left (x +1\right ) \HeunC \left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )-8 \left (x -1\right ) \left (c_{1} \HeunCPrime \left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )-\frac {\left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \HeunCPrime \left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )}{4}\right )}{4 \left (x +1\right ) \left (c_{1} \HeunC \left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )-\frac {\left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \HeunC \left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{x +1}\right )}{4}\right ) a}\right \}\]