\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =x/2+1+ \left ( y \left ( x \right ) \right ) ^{2}+1/4\,{x}^{2}y \left ( x \right ) -xy \left ( x \right ) -1/8\,{x}^{4}+1/8\,{x}^{3}+1/4\,{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}-3/4\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3/2\,x \left ( y \left ( x \right ) \right ) ^{2}+3/16\,y \left ( x \right ) {x}^{4}+3/4\,{x}^{3}y \left ( x \right ) -{\frac {{x}^{6}}{64}}-{\frac {3\,{x}^{5}}{32}}=0} \]
Mathematica: cpu = 0.099513 (sec), leaf count = 102 \[ \text {Solve}\left [-\frac {31}{3} \text {RootSum}\left [-31 \text {$\#$1}^3+3\ 2^{2/3} \sqrt [3]{31} \text {$\#$1}-31\& ,\frac {\log \left (\sqrt [3]{\frac {2}{31}} \left (\frac {1}{4} \left (-3 x^2-6 x+4\right )+3 y(x)\right )-\text {$\#$1}\right )}{2^{2/3} \sqrt [3]{31}-31 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} \left (\frac {31}{2}\right )^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.063 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{4}}+{\frac {x}{2}}+{\it RootOf} \left ( -x+2\,\int ^{{\it \_Z}}\! \left ( 2\,{{\it \_a}}^{3}+2\, {{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]