\[ y(x) y''(x)^2-a e^{2 x}=0 \] ✗ Mathematica : cpu = 20.252 (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 = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \left (\textit {\_a} \,{\mathrm e}^{\int \frac {2 \textit {\_}b\left (\textit {\_a} \right )}{3}d \textit {\_a} +\frac {2 c_{1}}{3}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=-\frac {\left (-4 \textit {\_a}^{2}+9 \sqrt {a \textit {\_a}}\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{9 \textit {\_a}}+\frac {4 \textit {\_}b\left (\textit {\_a} \right )^{2}}{3}\right \}, \left \{\textit {\_a} =y \relax (x ) {\mathrm e}^{-\frac {2 x}{3}}, \textit {\_}b\left (\textit {\_a} \right )=-\frac {3 \,{\mathrm e}^{\frac {2 x}{3}}}{-3 \frac {d}{d x}y \relax (x )+2 y \relax (x )}\right \}, \left \{x =\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}, y \relax (x )=\textit {\_a} \,{\mathrm e}^{\int \frac {2 \textit {\_}b\left (\textit {\_a} \right )}{3}d \textit {\_a} +\frac {2 c_{1}}{3}}\right \}\right ]\]