\[ y(x) (2 l x (-n+p-1)+2 l p+m)+2 \left (x (-2 l+n+1)-l x^2+n+1\right ) y'(x)+x (x+2) y''(x)=0 \] ✓ Mathematica : cpu = 0.476033 (sec), leaf count = 148
\[\left \{\left \{y(x)\to c_2 \left (-\frac {x}{2}-1\right )^{\frac {n}{2}+\frac {1}{2}} x^{-n} (x+2)^{-\frac {n}{2}-\frac {1}{2}} \text {HeunC}\left [-4 l n-2 l p-m+n^2+n,-4 l (p-1),1-n,n+1,4 l,-\frac {x}{2}\right ]+c_1 \left (-\frac {x}{2}-1\right )^{\frac {n}{2}+\frac {1}{2}} (x+2)^{-\frac {n}{2}-\frac {1}{2}} \text {HeunC}\left [-2 l p-m,4 l (n-p+1),n+1,n+1,4 l,-\frac {x}{2}\right ]\right \}\right \}\] ✓ Maple : cpu = 0.302 (sec), leaf count = 105
\[\left \{y \left (x \right ) = \left (c_{2} x^{-n} \HeunC \left (4 l , -n , n , -4 l p , -\frac {n^{2}}{2}+\frac {\left (4 n +4 p +4\right ) l}{2}+m -n , -\frac {x}{2}\right )+c_{1} \HeunC \left (4 l , n , n , -4 l p , -\frac {n^{2}}{2}+\frac {\left (4 n +4 p +4\right ) l}{2}+m -n , -\frac {x}{2}\right )\right ) \left (x +2\right )^{-\frac {n}{2}-\frac {1}{2}} \left (-\frac {x}{2}-1\right )^{\frac {n}{2}+\frac {1}{2}}\right \}\]