\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/4+1+ \left ( y \left ( x \right ) \right ) ^{2}+{\frac {7\,{x}^{2}y \left ( x \right ) }{16}}-1/2\,xy \left ( x \right ) +{\frac {5\,{x}^{4}}{128}}-{\frac {5\,{x}^{3}}{64}}+1/16\,{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}+3/8\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3/4\,x \left ( y \left ( x \right ) \right ) ^{2}+{\frac {3\,y \left ( x \right ) {x}^{4}}{64}}-3/16\,{x}^{3}y \left ( x \right ) +{\frac {{x}^{6}}{512}}-{\frac {3\,{x}^{5}}{256}}=0} \]
Mathematica: cpu = 0.094012 (sec), leaf count = 99 \[ \text {Solve}\left [-\frac {89}{3} \text {RootSum}\left [-89 \text {$\#$1}^3+6 \sqrt [3]{178} \text {$\#$1}-89\& ,\frac {\log \left (\frac {2^{2/3} \left (\frac {1}{8} \left (3 x^2-6 x+8\right )+3 y(x)\right )}{\sqrt [3]{89}}-\text {$\#$1}\right )}{2 \sqrt [3]{178}-89 \text {$\#$1}^2}\& \right ]=c_1+\frac {89^{2/3} x}{18 \sqrt [3]{2}},y(x)\right ] \]
Maple: cpu = 0.046 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{8}}+{\frac {x}{4}}+{ \it RootOf} \left ( -x+4\,\int ^{{\it \_Z}}\! \left ( 4\,{{\it \_a}}^{3} +4\,{{\it \_a}}^{2}+3 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]