\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{x}^{r} \left ( y \left ( x \right ) \right ) ^{n}=0} \]
Mathematica: cpu = 0.037505 (sec), leaf count = 20 \[ \text {DSolve}\left [a x^r y(x)^n+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 3.479 (sec), leaf count = 184 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {{\it \_a}}^{n}a{n}^{2}-2\, {{\it \_a}}^{n}an+{\it \_a}\,rn+{\it \_a}\,{r}^{2}+{{\it \_a}}^{n}a+2 \,{\it \_a}\,n+3\,{\it \_a}\,r+2\,{\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{ \left ( r+2 \right ) ^{2}}}+{ \frac { \left ( 2\,r+n+3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{r+2}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {r+2}{n-1}}},{\it \_b} \left ( {\it \_a} \right ) = -{\frac {r+2}{nx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) r-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) } \left ( {x}^{{\frac {r+2}{n-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a } \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{ r+2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]