\[ y(x) y''(x)^2-a e^{2 x}=0 \] ✗ Mathematica : cpu = 20.4935 (sec), leaf count = 0 , could not solve
DSolve[-(a*E^(2*x)) + y[x]*Derivative[2][y][x]^2 == 0, y[x], x]
✓ Maple : cpu = 1.201 (sec), leaf count = 117
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{\frac {2 c_{1}}{3}+\int \frac {2 \textit {\_}b\left (\textit {\_a} \right )}{3}d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=-\frac {\left (-4 \textit {\_a}^{2}+9 \sqrt {\textit {\_a} a}\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{9 \textit {\_a}}+\frac {4 \textit {\_}b\left (\textit {\_a} \right )^{2}}{3}\right \}, \left \{\textit {\_a} ={\mathrm e}^{-\frac {2 x}{3}} y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=-\frac {3 \,{\mathrm e}^{\frac {2 x}{3}}}{-3 \frac {d}{d x}y \left (x \right )+2 y \left (x \right )}\right \}, \left \{x =c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} , y \left (x \right )=\textit {\_a} \,{\mathrm e}^{\frac {2 c_{1}}{3}+\int \frac {2 \textit {\_}b\left (\textit {\_a} \right )}{3}d \textit {\_a}}\right \}\right ]\right )\right \}\]