\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}+2\,y \left ( x \right ) +x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) +x \right ) ^{2} \left ( y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) \left ( 1+y \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 0.624079 (sec), leaf count = 107 \[ \left \{\left \{y(x)\to \frac {-\sqrt {\left (-c_1 x+x^2-1\right ){}^2+4 \left (x-c_1\right )}+c_1 x-x^2+1}{2 \left (x-c_1\right )}\right \},\left \{y(x)\to \frac {\sqrt {\left (-c_1 x+x^2-1\right ){}^2+4 \left (x-c_1\right )}+c_1 x-x^2+1}{2 \left (x-c_1\right )}\right \}\right \} \]
Maple: cpu = 0.140 (sec), leaf count = 120 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}-4\,x} \left ( -{ \it \_C1}\,x+2\,{x}^{2}-2+\sqrt {{{\it \_C1}}^{2}{x}^{2}-4\,{x}^{3}{ \it \_C1}+4\,{x}^{4}+4\,{\it \_C1}\,x-8\,{x}^{2}-8\,{\it \_C1}+16\,x+4 } \right ) },y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}-4\,x} \left ( {\it \_C1}\,x-2\,{x}^{2}+\sqrt {{{\it \_C1}}^{2}{x}^{2}-4\,{x} ^{3}{\it \_C1}+4\,{x}^{4}+4\,{\it \_C1}\,x-8\,{x}^{2}-8\,{\it \_C1}+16 \,x+4}+2 \right ) } \right \} \]