\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x \left ( -x-1+{x}^{2}-2\,{x}^{2}y \left ( x \right ) +2\,{x}^{4} \right ) }{ \left ( {x}^{2}-y \left ( x \right ) \right ) \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 19.683499 (sec), leaf count = 487 \[ \text {Solve}\left [-\frac {2\ 2^{2/3} \left (2-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}\right ) \left (\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}+4\right ) \left (\left (1-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{2 \sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}\right ) \log \left (\frac {\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}+4}{2 \sqrt [3]{2}}\right )+\left (\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{2 \sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}-1\right ) \log \left (\frac {2-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}}{\sqrt [3]{2}}\right )+3\right )}{9 \left (-\frac {\left (2 x^2-2 y(x)+3\right )^3}{\left (x^2-y(x)\right )^3}+\frac {12 x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}-16\right )}=c_1+\frac {4\ 2^{2/3} \left (x^3 \left (x^2-x-1\right )^3\right )^{2/3} \left (x \left (x^2-3 x+3\right )-3 \log (x+1)\right )}{27 x^2 \left (-x^2+x+1\right )^2},y(x)\right ] \]
Maple: cpu = 0.437 (sec), leaf count = 191 \[ \left \{ y \left ( x \right ) ={1 \left ( 4\,{x}^{2}{{\rm e}^{{\it RootOf } \left ( 8\,{x}^{3}{{\rm e}^{{\it \_Z}}}-24\,{{\rm e}^{{\it \_Z}}}{x}^ {2}-36\,{x}^{3}+6\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) {{\rm e}^{{\it \_Z}}}+18\,{\it \_C1 }\,{{\rm e}^{{\it \_Z}}}-6\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+24\,x{ {\rm e}^{{\it \_Z}}}+108\,{x}^{2}-27\,\ln \left ( {\frac {2\,{{\rm e}^ {{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) -81\,{\it \_C1}+27 \,{\it \_Z}-108\,x+27 \right ) }}-18\,{x}^{2}-9 \right ) \left ( 4\,{ {\rm e}^{{\it RootOf} \left ( 8\,{x}^{3}{{\rm e}^{{\it \_Z}}}-24\,{ {\rm e}^{{\it \_Z}}}{x}^{2}-36\,{x}^{3}+6\,\ln \left ( {\frac {2\,{ {\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) {{\rm e}^{{ \it \_Z}}}+18\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}-6\,{\it \_Z}\,{ {\rm e}^{{\it \_Z}}}+24\,x{{\rm e}^{{\it \_Z}}}+108\,{x}^{2}-27\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) -81\,{\it \_C1}+27\,{\it \_Z}-108\,x+27 \right ) }}-18 \right ) ^{-1}} \right \} \]