\[ \boxed { y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) +b{{\rm e}^{x}}-2\,a=0} \]
Mathematica: cpu = 30.060317 (sec), leaf count = 26 \[ \text {DSolve}\left [a y(x)-2 a+b e^x+y(x) y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.780 (sec), leaf count = 0 \[ \text {could not solve} \]