\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x \left ( y \left ( x \right ) \right ) ^{n}=0} \]
Mathematica: cpu = 0.037005 (sec), leaf count = 26 \[ \text {DSolve}\left [-x y(x)^n+x y''(x)+2 y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.593 (sec), leaf count = 151 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( -{\frac {{{\it \_a}}^{n}{n}^{2}}{4} }+{\frac {{{\it \_a}}^{n}n}{2}}-{\frac {{\it \_a}\,n}{2}}-{\frac {{{ \it \_a}}^{n}}{4}}+{\frac {3\,{\it \_a}}{2}} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( -{\frac {n}{2}}+{ \frac {5}{2}} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{2\, \left ( n-1 \right ) ^{-1}},{\it \_b} \left ( {\it \_a} \right ) =-2\,{ \frac {1}{nx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) } \left ( { x}^{2\, \left ( n-1 \right ) ^{-1}} \right ) ^{-1}} \right \} , \left \{ x= {{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) n}{2}}+{\frac {\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}{2}}+{\frac {{\it \_C1}}{ 2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]