\[ \boxed { \left ( 4\, \left ( y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) +3\,{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}+6\,xy \left ( x \right ) +2\,{x}^{2}=0} \]
Mathematica: cpu = 0.029004 (sec), leaf count = 402 \[ \left \{\left \{y(x)\to \frac {\sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}{12 \sqrt [3]{2}}-\frac {33 x^2}{2\ 2^{2/3} \sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}-\frac {x}{4}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}{24 \sqrt [3]{2}}+\frac {33 \left (1+i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}-\frac {x}{4}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}{24 \sqrt [3]{2}}+\frac {33 \left (1-i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{\sqrt {\left (432 e^{3 c_1}+54 x^3\right ){}^2+3881196 x^6}+432 e^{3 c_1}+54 x^3}}-\frac {x}{4}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 431 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {1}{ 4}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{ x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}-{\frac {11\,{{\it \_C1}}^{2}{x }^{2}}{4}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333 \,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}}-{\frac {{ \it \_C1}\,x}{4}} \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( -{\frac {1}{8}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt { 333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}+{\frac { 11\,{{\it \_C1}}^{2}{x}^{2}}{8}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1} }^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^ {3}+16}}}}}-{\frac {{\it \_C1}\,x}{4}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{4}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}+{\frac {11\,{{\it \_C1}}^{2}{x}^{2}}{4}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2 \,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}} }} \right ) \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( -{\frac {1}{8}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt { 333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}+{\frac { 11\,{{\it \_C1}}^{2}{x}^{2}}{8}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1} }^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^ {3}+16}}}}}-{\frac {{\it \_C1}\,x}{4}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{4}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}+{\frac {11\,{{\it \_C1}}^{2}{x}^{2}}{4}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2 \,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}} }} \right ) \right ) } \right \} \]