\[ a^2 y(x)^n+x^4 y''(x)=0 \] ✗ Mathematica : cpu = 0.0320163 (sec), leaf count = 0 , could not solve
DSolve[a^2*y[x]^n + x^4*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.433 (sec), leaf count = 128
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (\left (n -1\right )^{2} a^{2} \textit {\_a}^{n} \textit {\_}b\left (\textit {\_a} \right )-2 \left (n -3\right ) \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )-2 n +10\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{4}\right \}, \left \{\textit {\_a} =x^{-\frac {2}{n -1}} y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {2 x^{\frac {2}{n -1}}}{\left (n -1\right ) x \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{\frac {\left (c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right ) \left (n -1\right )}{2}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]