\[ a x^r y(x)^n+y''(x)=0 \] ✗ Mathematica : cpu = 0.0277776 (sec), leaf count = 0 , could not solve
DSolve[a*x^r*y[x]^n + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 4.38 (sec), leaf count = 151
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( a{\it \_b} \left ( {\it \_a} \right ) \left ( n-1 \right ) ^{2}{{\it \_a}}^{n}+ \left ( {\it \_a}\, \left ( r+1+n \right ) {\it \_b} \left ( {\it \_a} \right ) +2\,r+n+3 \right ) \left ( r+2 \right ) \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{ \left ( r+2 \right ) ^{2}}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {r+2}{n-1}}},{\it \_b} \left ( {\it \_a} \right ) ={\frac {-r-2}{ \left ( n-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \left ( r+2 \right ) } \left ( {x}^{{\frac {r+2}{n-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{r+2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]