\[ y(x) (2 l x (-n+p-1)+2 l p+m)+2 \left (x (-2 l+n+1)-l x^2+n+1\right ) y'(x)+x (x+2) y''(x)=0 \] ✗ Mathematica : cpu = 2.48822 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(-2 \unicode {f817} l-2 \unicode {f817} n l+2 \unicode {f817} p l+2 p l+m) \unicode {f818}(\unicode {f817})+2 \left (-l \unicode {f817}^2-2 l \unicode {f817}+n \unicode {f817}+\unicode {f817}+n+1\right ) \unicode {f818}'(\unicode {f817})+\unicode {f817} (\unicode {f817}+2) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.246 (sec), leaf count = 105
\[ \left \{ y \left ( x \right ) = \left ( x+2 \right ) ^{-{\frac {n}{2}}-{\frac {1}{2}}} \left ( -{\frac {x}{2}}-1 \right ) ^{{\frac {n}{2}}+{\frac {1}{2}}} \left ( {x}^{-n}{\it HeunC} \left ( 4\,l,-n,n,-4\,pl,{\frac { \left ( 4\,n+4\,p+4 \right ) l}{2}}-{\frac {{n}^{2}}{2}}+m-n,-{\frac {x}{2}} \right ) {\it \_C2}+{\it HeunC} \left ( 4\,l,n,n,-4\,pl,{\frac { \left ( 4\,n+4\,p+4 \right ) l}{2}}-{\frac {{n}^{2}}{2}}+m-n,-{\frac {x}{2}} \right ) {\it \_C1} \right ) \right \} \]