\[ y(x) y''(x)-a x^2=0 \] ✗ Mathematica : cpu = 19.3692 (sec), leaf count = 0 , could not solve
DSolve[-(a*x^2) + y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.707 (sec), leaf count = 100
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{2 c_{1}+\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (2 \textit {\_a}^{2}-a \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{\textit {\_a}}+3 \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =\frac {y \left (x \right )}{x^{2}}, \textit {\_}b\left (\textit {\_a} \right )=\frac {x^{2}}{x \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{2 c_{1}+\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]