\[ \boxed { 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1+2\,x \left ( y \left ( x \right ) \right ) ^{2}+a \left ( y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 1.481688 (sec), leaf count = 37 \[ \text {DSolve}\left [a y(x)^3+2 y(x) y''(x)-y'(x)^2+2 x y(x)^2+1=0,y(x),x\right ] \]
Maple: cpu = 1.841 (sec), leaf count = 0 \[ \text {could not solve} \]