\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =x/2+1/2+{x}^{2}\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0} \]
Mathematica: cpu = 0.196525 (sec), leaf count = 37 \[ \left \{\left \{y(x)\to \frac {1}{36} \left (24 c_1 x^3-36 c_1^2-4 x^6+9 x^2+18 x+9\right )\right \}\right \} \]
Maple: cpu = 0.188 (sec), leaf count = 26 \[ \left \{ {\it \_C1}-{\frac {2\,{x}^{3}}{3}}-\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]