\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {14\,xy \left ( x \right ) +12+2\,x+{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+6\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2} \left ( xy \left ( x \right ) +2+x \right ) }}=0} \]
Mathematica: cpu = 0.016502 (sec), leaf count = 76 \[ \left \{\left \{y(x)\to \frac {1}{x^3 \left (\frac {1}{x^3}-\frac {1}{x^3 \sqrt {c_1-2 x}}\right )}-\frac {x+2}{x}\right \},\left \{y(x)\to \frac {1}{x^3 \left (\frac {1}{x^3 \sqrt {c_1-2 x}}+\frac {1}{x^3}\right )}-\frac {x+2}{x}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 65 \[ \left \{ y \left ( x \right ) =-{\frac {1}{x} \left ( 2\,\sqrt {{\it \_C1 }-2\,x}-x-2 \right ) \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{x} \left ( 2\,\sqrt {{\it \_C1}-2\,x}+x+ 2 \right ) \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) ^{-1}} \right \} \]