\[ a x y'(x)+y(x) \left (b x^2+c x+d\right )+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.250225 (sec), leaf count = 238
\[\left \{\left \{y(x)\to c_2 \left (\frac {x}{2}-\frac {1}{2}\right )^{a/4} \left (x^2-1\right )^{-a/4} \left (\frac {x}{2}+\frac {1}{2}\right )^{1-\frac {a}{4}} e^{\sqrt {-b} x} \text {HeunC}\left [\frac {1}{4} a \left (a-4 \sqrt {-b}-2\right )-b+4 \sqrt {-b}+c-d,2 \left (2 \sqrt {-b}+c\right ),2-\frac {a}{2},\frac {a}{2},4 \sqrt {-b},\frac {x}{2}+\frac {1}{2}\right ]+c_1 ((x-1) (x+1))^{a/4} \left (x^2-1\right )^{-a/4} e^{\sqrt {-b} x} \text {HeunC}\left [a \sqrt {-b}-b+c-d,2 \left (a \sqrt {-b}+c\right ),\frac {a}{2},\frac {a}{2},4 \sqrt {-b},\frac {x}{2}+\frac {1}{2}\right ]\right \}\right \}\] ✓ Maple : cpu = 0.177 (sec), leaf count = 134
\[y \relax (x ) = \left (x^{2}-1\right )^{-\frac {a}{4}} {\mathrm e}^{\sqrt {-b}\, x} \left (\left (-\frac {1}{2}+\frac {x}{2}\right )^{\frac {a}{4}} \HeunC \left (4 \sqrt {-b}, 1-\frac {a}{2}, \frac {a}{2}-1, 2 c , d -c -\frac {a^{2}}{8}+b +\frac {1}{2}, \frac {1}{2}+\frac {x}{2}\right ) \left (\frac {1}{2}+\frac {x}{2}\right )^{1-\frac {a}{4}} c_{2}+\left (\left (x -1\right ) \left (1+x \right )\right )^{\frac {a}{4}} \HeunC \left (4 \sqrt {-b}, \frac {a}{2}-1, \frac {a}{2}-1, 2 c , d -c -\frac {a^{2}}{8}+b +\frac {1}{2}, \frac {1}{2}+\frac {x}{2}\right ) c_{1}\right )\]