\[ y(x) y''(x)-a x^2=0 \] ✗ Mathematica : cpu = 14.0384 (sec), leaf count = 0
, could not solve
DSolve[-(a*x^2) + y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \left (\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (2 \textit {\_a}^{2}-a \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{\textit {\_a}}+3 \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =\frac {y \relax (x )}{x^{2}}, \textit {\_}b\left (\textit {\_a} \right )=\frac {x^{2}}{x \left (\frac {d}{d x}y \relax (x )\right )-2 y \relax (x )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \relax (x )=\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right \}\right ]\]