\[ a^2 y(x)^n+x^4 y''(x)=0 \] ✗ Mathematica : cpu = 0.0309196 (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 = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \left (\textit {\_a} \,{\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (\frac {a^{2} n^{2} \textit {\_a}^{n}}{4}-\frac {a^{2} n \,\textit {\_a}^{n}}{2}+\frac {a^{2} \textit {\_a}^{n}}{4}-\frac {\textit {\_a} n}{2}+\frac {3 \textit {\_a}}{2}\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (-\frac {n}{2}+\frac {5}{2}\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \relax (x ) x^{-\frac {2}{n -1}}, \textit {\_}b\left (\textit {\_a} \right )=-\frac {2 x^{\frac {2}{n -1}}}{-n x \left (\frac {d}{d x}y \relax (x )\right )+x \left (\frac {d}{d x}y \relax (x )\right )+2 y \relax (x )}\right \}, \left \{x ={\mathrm e}^{\frac {\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right ) n}{2}-\frac {\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )}{2}-\frac {c_{1}}{2}}, y \relax (x )=\textit {\_a} \,{\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right \}\right ]\]