\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/2+1+ \left ( y \left ( x \right ) \right ) ^{2}+7/2\,{x}^{2}y \left ( x \right ) -2\,xy \left ( x \right ) +{\frac {13\,{x}^{4}}{16}}-3/2\,{x}^{3}+{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}+3/4\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3\,x \left ( y \left ( x \right ) \right ) ^{2}+3/16\,y \left ( x \right ) {x}^{4}-3/2\,{x}^{3}y \left ( x \right ) +{\frac {{x}^{6}}{64}}-3/16\,{x}^{5}=0} \]
Mathematica: cpu = 49.448279 (sec), leaf count = 246 \[ \text {Solve}\left [-\frac {\sqrt [3]{2} \left (\frac {\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)}{\sqrt [3]{2}}+2^{2/3}\right ) \left (2^{2/3}-2^{2/3} \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )\right ) \left (\left (\frac {1}{4} \left (-3 x^2+12 x-4\right )-3 y(x)+1\right ) \log \left (\frac {\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)}{\sqrt [3]{2}}+2^{2/3}\right )+\left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)-1\right ) \log \left (2^{2/3}-2^{2/3} \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )\right )+3\right )}{9 \left (-\left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )^3+3 \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )-2\right )}=c_1+\frac {1}{9} 2^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.156 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( \ln \left ( {{\rm e}^{{\it \_Z}}}-4 \right ) {{\rm e}^{{\it \_Z}}}+{ \it \_C1}\,{{\rm e}^{{\it \_Z}}}-{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+x{ {\rm e}^{{\it \_Z}}}-4\,\ln \left ( {{\rm e}^{{\it \_Z}}}-4 \right ) -4 \,{\it \_C1}+4\,{\it \_Z}-4\,x+4 \right ) }}}{4}}-1-{\frac {{x}^{2}}{4} }+x \right \} \]