\[ a x^r y(x)^n+y''(x)=0 \] ✗ Mathematica : cpu = 0.0375863 (sec), leaf count = 0 , could not solve
DSolve[a*x^r*y[x]^n + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 3.185 (sec), leaf count = 184
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {{\it \_a}}^{n}a{n}^{2}-2\,{{\it \_a}}^{n}an+{\it \_a}\,rn+{\it \_a}\,{r}^{2}+{{\it \_a}}^{n}a+2\,{\it \_a}\,n+3\,{\it \_a}\,r+2\,{\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{ \left ( r+2 \right ) ^{2}}}+{\frac { \left ( 2\,r+n+3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{r+2}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {r+2}{n-1}}},{\it \_b} \left ( {\it \_a} \right ) =-{\frac {r+2}{nx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) r-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) } \left ( {x}^{{\frac {r+2}{n-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{r+2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]