\[ a x y'(x)+y(x) \left (b x^2+c x+d\right )+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.251891 (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 = 1.224 (sec), leaf count = 134
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {-b}x}} \left ( {x}^{2}-1 \right ) ^{-{\frac {a}{4}}} \left ( \left ( {\frac {1}{2}}+{\frac {x}{2}} \right ) ^{1-{\frac {a}{4}}} \left ( -{\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {a}{4}}}{\it HeunC} \left ( 4\,\sqrt {-b},1-{\frac {a}{2}},{\frac {a}{2}}-1,2\,c,d-c-{\frac {{a}^{2}}{8}}+b+{\frac {1}{2}},{\frac {1}{2}}+{\frac {x}{2}} \right ) {\it \_C2}+{\it HeunC} \left ( 4\,\sqrt {-b},{\frac {a}{2}}-1,{\frac {a}{2}}-1,2\,c,d-c-{\frac {{a}^{2}}{8}}+b+{\frac {1}{2}},{\frac {1}{2}}+{\frac {x}{2}} \right ) \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) ^{{\frac {a}{4}}}{\it \_C1} \right ) \right \} \]