\[ a x^r y(x)^n+y''(x)=0 \] ✗ Mathematica : cpu = 0.0407634 (sec), leaf count = 0 , could not solve
DSolve[a*x^r*y[x]^n + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 4.318 (sec), leaf count = 151
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (\left (n -1\right )^{2} a \,\textit {\_a}^{n} \textit {\_}b\left (\textit {\_a} \right )+\left (\left (n +r +1\right ) \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+n +2 r +3\right ) \left (r +2\right )\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{\left (r +2\right )^{2}}\right \}, \left \{\textit {\_a} =x^{\frac {r +2}{n -1}} y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {\left (-r -2\right ) x^{-\frac {r +2}{n -1}}}{\left (n -1\right ) x \left (\frac {d}{d x}y \left (x \right )\right )+\left (r +2\right ) y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{-\frac {\left (c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right ) \left (n -1\right )}{r +2}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]