\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,a \left ( y \left ( x \right ) \right ) ^{2}+b \left ( y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 46.194866 (sec), leaf count = 43 \[ \text {DSolve}\left [a y(x) y'(x)-2 a y(x)^2+b y(x)^3+y(x) y''(x)-y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 2.106 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-{\it \_a}\,{ \it \_b} \left ( {\it \_a} \right ) a-b{{\it \_a}}^{3}+2\,{{\it \_a}}^{2 }a}{{\it \_a}}}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{ \it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]