\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+{{\rm e}^{x}}y \left ( x \right ) \left ( c \left ( y \left ( x \right ) \right ) ^{2}+d \right ) +{{\rm e}^{2\,x}} \left ( b+a \left ( y \left ( x \right ) \right ) ^{4} \right ) =0} \]
Mathematica: cpu = 5.336178 (sec), leaf count = 50 \[ \text {DSolve}\left [e^{2 x} \left (a y(x)^4+b\right )+e^x y(x) \left (c y(x)^2+d\right )+y(x) y''(x)-y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 3.448 (sec), leaf count = 0 \[ \text {could not solve} \]