\[ a x^m y(x)^n+x y''(x)+2 y'(x)=0 \] ✗ Mathematica : cpu = 0.202213 (sec), leaf count = 0 , could not solve
DSolve[a*x^m*y[x]^n + 2*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 3.128 (sec), leaf count = 155
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (\left (n -1\right )^{2} a \,\textit {\_a}^{n} \textit {\_}b\left (\textit {\_a} \right )+\left (m +1\right ) \left (\left (m -n +2\right ) \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+2 m -n +3\right )\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{\left (m +1\right )^{2}}\right \}, \left \{\textit {\_a} =x^{\frac {m +1}{n -1}} y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {\left (-m -1\right ) x^{-\frac {m +1}{n -1}}}{\left (n -1\right ) x \left (\frac {d}{d x}y \left (x \right )\right )+\left (m +1\right ) y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{-\frac {\left (c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right ) \left (n -1\right )}{m +1}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]