\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}- \left ( -1+ay \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}-2\,{b}^{2} \left ( y \left ( x \right ) \right ) ^{3}+ay \left ( x \right ) =0} \]
Mathematica: cpu = 61.278281 (sec), leaf count = 56 \[ \text {DSolve}\left [2 a^2 y(x)^2-(a y(x)-1) y'(x)+a y(x)-2 b^2 y(x)^3+y(x) y''(x)-y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 2.792 (sec), leaf count = 84 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\frac { 2\,{b}^{2}{{\it \_a}}^{3}-2\,{{\it \_a}}^{2}{a}^{2}+{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) a+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-a{\it \_a}-{\it \_b} \left ( {\it \_a} \right ) }{{\it \_a}}}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]