\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =x/2+1/2+\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }+{x}^{2}\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }+{x}^{3}\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0} \]
Mathematica: cpu = 0.365046 (sec), leaf count = 69 \[ \left \{\left \{y(x)\to \frac {1}{144} \left (72 c_1 x^4+96 c_1 x^3+288 c_1 x-144 c_1^2-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4-108 x^2+72 x+36\right )\right \}\right \} \]
Maple: cpu = 0.265 (sec), leaf count = 36 \[ \left \{ -{\frac {1}{2}\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }}- {\frac {{x}^{4}}{4}}-{\frac {{x}^{3}}{3}}-x-{\it \_C1}=0 \right \} \]