\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +b{{\rm e}^{y \left ( x \right ) }}-2\,a=0} \]
Mathematica: cpu = 30.684396 (sec), leaf count = 26 \[ \text {DSolve}\left [a y'(x)-2 a+b e^{y(x)}+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 1.107 (sec), leaf count = 56 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +a{\it \_b} \left ( {\it \_a} \right ) +b{{\rm e}^{{\it \_a}}}-2\,a=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]