\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a{x}^{m} \left ( y \left ( x \right ) \right ) ^{n}=0} \]
Mathematica: cpu = 0.537568 (sec), leaf count = 28 \[ \text {DSolve}\left [a x^m y(x)^n+x y''(x)+2 y'(x)=0,y(x),x\right ] \]
Maple: cpu = 2.355 (sec), leaf count = 185 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {{\it \_a}}^{n}a{n}^{2}-2\, {{\it \_a}}^{n}an+{\it \_a}\,{m}^{2}-{\it \_a}\,mn+{{\it \_a}}^{n}a+3 \,{\it \_a}\,m-{\it \_a}\,n+2\,{\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{ \left ( m+1 \right ) ^{2}}}+{ \frac { \left ( 2\,m-n+3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{m+1}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {m+1}{n-1}}},{\it \_b} \left ( {\it \_a} \right ) = -{\frac {m+1}{nx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) m-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) } \left ( {x}^{{\frac {m+1}{n-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a } \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{ m+1}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]