\[ \boxed { 2\, \left ( x-{\it a1} \right ) \left ( x-{\it a2} \right ) \left ( x-{\it a3} \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( 9\,{x}^{2}-6\, \left ( {\it a1}+{\it a2}+{\it a3} \right ) x+3\,{\it a1}\,{\it a2}+3\,{\it a1}\,{\it a3}+3\,{\it a2}\,{\it a3} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\, \left ( \left ( {n}^{2}+n-3 \right ) x+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -n \left ( n+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 72.774241 (sec), leaf count = 167 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-n (n+1) \unicode {f818}(\unicode {f817})-2 \left (\unicode {f817} n^2+\unicode {f817} n-3 \unicode {f817}+b\right ) \unicode {f818}'(\unicode {f817})+3 \left (3 \unicode {f817}^2-2 \text {a1} \unicode {f817}-2 \text {a2} \unicode {f817}-2 \text {a3} \unicode {f817}+\text {a1} \text {a2}+\text {a1} \text {a3}+\text {a2} \text {a3}\right ) \unicode {f818}''(\unicode {f817})-2 (\text {a1}-\unicode {f817}) (\text {a2}-\unicode {f817}) (\text {a3}-\unicode {f817}) \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \} \]
Maple: cpu = 0.374 (sec), leaf count = 279 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\it HeunG} \left ( { \frac {-{\it a3}+{\it a1}}{-{\it a2}+{\it a1}}},-{\frac {{\it a1}\,{n} ^{2}+{\it a1}\,n-{\it a1}-{\it a2}-{\it a3}+b}{-4\,{\it a2}+4\,{\it a1 }}},-{\frac {n}{2}},{\frac {n}{2}}+{\frac {1}{2}},{\frac {1}{2}},{ \frac {1}{2}},{\frac {-x+{\it a1}}{-{\it a2}+{\it a1}}} \right ) \right ) ^{2}+{\it \_C2}\, \left ( {\it HeunG} \left ( {\frac {-{\it a3} +{\it a1}}{-{\it a2}+{\it a1}}},-{\frac {{\it a1}\,{n}^{2}+{\it a1}\,n -3\,{\it a1}+b}{-4\,{\it a2}+4\,{\it a1}}},{\frac {n}{2}}+1,-{\frac {n }{2}}+{\frac {1}{2}},{\frac {3}{2}},{\frac {1}{2}},{\frac {-x+{\it a1} }{-{\it a2}+{\it a1}}} \right ) \right ) ^{2} \left ( -x+{\it a1} \right ) +{\it \_C3}\,{\it HeunG} \left ( {\frac {-{\it a3}+{\it a1}}{- {\it a2}+{\it a1}}},-{\frac {{\it a1}\,{n}^{2}+{\it a1}\,n-{\it a1}-{ \it a2}-{\it a3}+b}{-4\,{\it a2}+4\,{\it a1}}},-{\frac {n}{2}},{\frac {n}{2}}+{\frac {1}{2}},{\frac {1}{2}},{\frac {1}{2}},{\frac {-x+{\it a1}}{-{\it a2}+{\it a1}}} \right ) {\it HeunG} \left ( {\frac {-{\it a3} +{\it a1}}{-{\it a2}+{\it a1}}},-{\frac {{\it a1}\,{n}^{2}+{\it a1}\,n -3\,{\it a1}+b}{-4\,{\it a2}+4\,{\it a1}}},{\frac {n}{2}}+1,-{\frac {n }{2}}+{\frac {1}{2}},{\frac {3}{2}},{\frac {1}{2}},{\frac {-x+{\it a1} }{-{\it a2}+{\it a1}}} \right ) \sqrt {-x+{\it a1}} \right \} \]