\[ \boxed { x \left ( x+2 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\, \left ( n+1+ \left ( n+1-2\,l \right ) x-l{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 2\,l \left ( p-n-1 \right ) x+2\,pl+m \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 2.666839 (sec), leaf count = 82 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(-2 \unicode {f817} l-2 \unicode {f817} n l+2 \unicode {f817} p l+2 p l+m) \unicode {f818}(\unicode {f817})+2 \left (-l \unicode {f817}^2-2 l \unicode {f817}+n \unicode {f817}+\unicode {f817}+n+1\right ) \unicode {f818}'(\unicode {f817})+\unicode {f817} (\unicode {f817}+2) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.171 (sec), leaf count = 124 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunC} \left ( 4\,l,n,n,- 4\,pl,{\frac { \left ( 4\,n+4\,p+4 \right ) l}{2}}-{\frac {{n}^{2}}{2}}+ m-n,-{\frac {x}{2}} \right ) \left ( x+2 \right ) ^{-{\frac {n}{2}}-{ \frac {1}{2}}} \left ( -{\frac {x}{2}}-1 \right ) ^{{\frac {n}{2}}+{ \frac {1}{2}}}+{\it \_C2}\,{\it HeunC} \left ( 4\,l,-n,n,-4\,pl,{\frac { \left ( 4\,n+4\,p+4 \right ) l}{2}}-{\frac {{n}^{2}}{2}}+m-n,-{\frac { x}{2}} \right ) {x}^{-n} \left ( x+2 \right ) ^{-{\frac {n}{2}}-{\frac {1 }{2}}} \left ( -{\frac {x}{2}}-1 \right ) ^{{\frac {n}{2}}+{\frac {1}{2} }} \right \} \]