\[ y'(x)=\frac {x \left (-2 x^2 y(x)+2 x^4+x^2-x-1\right )}{(x+1) \left (x^2-y(x)\right )} \] ✓ Mathematica : cpu = 19.0067 (sec), leaf count = 488
\[\text {Solve}\left [\frac {\left (2-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}\right ) \left (\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}+4\right ) \left (\left (1-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{2 \sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}\right ) \log \left (\frac {2-\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}}{\sqrt [3]{2}}\right )+\left (\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{2 \sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}-1\right ) \log \left (\frac {\frac {x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{\sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}+4}{\sqrt [3]{2}}\right )-3\right )}{18 \sqrt [3]{2} \left (-\frac {\left (2 x^2-2 y(x)+3\right )^3}{8 \left (x^2-y(x)\right )^3}+\frac {3 x \left (x^2-x-1\right ) \left (2 x^2-2 y(x)+3\right )}{2 \sqrt [3]{x^3 \left (x^2-x-1\right )^3} \left (x^2-y(x)\right )}-2\right )}=\frac {4\ 2^{2/3} \left (x^3 \left (x^2-x-1\right )^3\right )^{2/3} \left (x \left (x^2-3 x+3\right )-3 \log (x+1)\right )}{27 x^2 \left (-x^2+x+1\right )^2}+c_1,y(x)\right ]\] ✓ Maple : cpu = 1.281 (sec), leaf count = 191
\[ \left \{ y \left ( x \right ) ={ \left ( 4\,{x}^{2}{{\rm e}^{{\it RootOf} \left ( 8\,{x}^{3}{{\rm e}^{{\it \_Z}}}-24\,{{\rm e}^{{\it \_Z}}}{x}^{2}-36\,{x}^{3}+6\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) {{\rm e}^{{\it \_Z}}}+18\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-6\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+24\,x{{\rm e}^{{\it \_Z}}}+108\,{x}^{2}-27\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) -81\,{\it \_C1}+27\,{\it \_Z}-108\,x+27 \right ) }}-18\,{x}^{2}-9 \right ) \left ( 4\,{{\rm e}^{{\it RootOf} \left ( 8\,{x}^{3}{{\rm e}^{{\it \_Z}}}-24\,{{\rm e}^{{\it \_Z}}}{x}^{2}-36\,{x}^{3}+6\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) {{\rm e}^{{\it \_Z}}}+18\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-6\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+24\,x{{\rm e}^{{\it \_Z}}}+108\,{x}^{2}-27\,\ln \left ( {\frac {2\,{{\rm e}^{{\it \_Z}}}-9}{ \left ( 1+x \right ) ^{4}}} \right ) -81\,{\it \_C1}+27\,{\it \_Z}-108\,x+27 \right ) }}-18 \right ) ^{-1}} \right \} \]