\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{3}-a{{\rm e}^{x}} \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.679086 (sec), leaf count = 78 \[ \text {Solve}\left [-i a e^x=\frac {2 e^{\frac {1}{2} \left (-i a e^x-\frac {i}{y(x)}\right )^2}}{2 c_1+\sqrt {2 \pi } \text {erfi}\left (\frac {-i a e^x-\frac {i}{y(x)}}{\sqrt {2}}\right )},y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 50 \[ \left \{ {\it \_C1}+{\frac {1}{a{{\rm e}^{x}}}{{\rm e}^{-{\frac { \left ( a{{\rm e}^{x}}+ \left ( y \left ( x \right ) \right ) ^{-1} \right ) ^{2}}{2}}}}}+{\frac {\sqrt {2}\sqrt {\pi }}{2}{\it Erf} \left ( {\frac { \left ( a{{\rm e}^{x}}+ \left ( y \left ( x \right ) \right ) ^{-1} \right ) \sqrt {2}}{2}} \right ) }=0 \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]