\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( b{x}^{2}+cx+d \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 2.122269 (sec), leaf count = 57 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (b \unicode {f817}^2+c \unicode {f817}+d\right ) \unicode {f818}(\unicode {f817})+\unicode {f817} a \unicode {f818}'(\unicode {f817})+\left (\unicode {f817}^2-1\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.172 (sec), leaf count = 150 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\sqrt {-b}x}} \left ( {x}^{2}-1 \right ) ^{-{\frac {a}{4}}} \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) ^{{\frac {a}{4}}}{\it HeunC} \left ( 4\,\sqrt {-b},{\frac {a}{2}}-1,{\frac {a}{2}}-1,2\,c,d-c-{ \frac {{a}^{2}}{8}}+b+{\frac {1}{2}},{\frac {1}{2}}+{\frac {x}{2}} \right ) +{\it \_C2}\,{{\rm e}^{\sqrt {-b}x}} \left ( {\frac {1}{2}}+{ \frac {x}{2}} \right ) ^{1-{\frac {a}{4}}} \left ( -{\frac {1}{2}}+{ \frac {x}{2}} \right ) ^{{\frac {a}{4}}} \left ( {x}^{2}-1 \right ) ^{-{ \frac {a}{4}}}{\it HeunC} \left ( 4\,\sqrt {-b},1-{\frac {a}{2}},{ \frac {a}{2}}-1,2\,c,d-c-{\frac {{a}^{2}}{8}}+b+{\frac {1}{2}},{\frac {1}{2}}+{\frac {x}{2}} \right ) \right \} \]