\[ y(x) y''(x)^2-a e^{2 x}=0 \] ✗ Mathematica : cpu = 20.2112 (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 = 3.276 (sec), leaf count = 117
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\it \_a} \left ( {{\rm e}^{-{\frac {2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}{3}}-{\frac {2\,{\it \_C1}}{3}}}} \right ) ^{-1}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =-{\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{9\,{\it \_a}} \left ( -4\,{{\it \_a}}^{2}+9\,\sqrt {{\it \_a}\,a} \right ) }+{\frac {4\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{3}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {{\rm e}^{-{\frac {2\,x}{3}}}},{\it \_b} \left ( {\it \_a} \right ) =-3\,{\frac {1}{{{\rm e}^{-2/3\,x}} \left ( -3\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) \right ) }} \right \} , \left \{ x=\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={{\it \_a} \left ( {{\rm e}^{-{\frac {2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}{3}}-{\frac {2\,{\it \_C1}}{3}}}} \right ) ^{-1}} \right \} ] \right ) \right \} \]