\[ \boxed { x \left ( y \left ( x \right ) +4 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) -2\,x=0} \]
Mathematica: cpu = 0.015502 (sec), leaf count = 114 \[ \left \{\left \{y(x)\to \frac {1}{x \left (\frac {1}{x^2+4 x}-\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {c_1-\frac {4}{x+4}}}\right )}-4\right \},\left \{y(x)\to \frac {1}{x \left (\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {c_1-\frac {4}{x+4}}}+\frac {1}{x^2+4 x}\right )}-4\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 147 \[ \left \{ y \left ( x \right ) =-{1 \left ( - \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\,x+4\,{\it \_C1}-4}{x+4}}}x+4\,{x}^{ 3/2}+16\,\sqrt {x} \right ) \left ( \left ( x+4 \right ) ^{{\frac {3}{2} }}\sqrt {{\frac {{\it \_C1}\,x+4\,{\it \_C1}-4}{x+4}}}+{x}^{{\frac {3} {2}}}+4\,\sqrt {x} \right ) ^{-1}},y \left ( x \right ) =-{1 \left ( \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\,x+4\,{ \it \_C1}-4}{x+4}}}x+4\,{x}^{3/2}+16\,\sqrt {x} \right ) \left ( - \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\,x+4\,{ \it \_C1}-4}{x+4}}}+{x}^{{\frac {3}{2}}}+4\,\sqrt {x} \right ) ^{-1}} \right \} \]