\[ \left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.0359012 (sec), leaf count = 382
\[\left \{\left \{y(x)\to \frac {1}{4} \left (\sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}-\frac {11 x^2}{\sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}}-x\right )\right \},\left \{y(x)\to \frac {1}{16} \left (2 i \left (\sqrt {3}+i\right ) \sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}+\frac {22 \left (1+i \sqrt {3}\right ) x^2}{\sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}}-4 x\right )\right \},\left \{y(x)\to \frac {1}{16} \left (-2 \left (1+i \sqrt {3}\right ) \sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}+\frac {22 \left (1-i \sqrt {3}\right ) x^2}{\sqrt [3]{2 \sqrt {4 e^{3 c_1} x^3+16 e^{6 c_1}+333 x^6}+8 e^{3 c_1}+x^3}}-4 x\right )\right \}\right \}\]
✓ Maple : cpu = 0.086 (sec), leaf count = 432
\[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {1}{4}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}-{\frac {11\,{{\it \_C1}}^{2}{x}^{2}}{4}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}}-{\frac {{\it \_C1}\,x}{4}} \right ) },y \left ( x \right ) =-{\frac {1}{8\,{\it \_C1}} \left ( 2\,{\it \_C1}\,x\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}+ \left ( 11\,i{{\it \_C1}}^{2}{x}^{2}+i \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}-11\,{{\it \_C1}}^{2}{x}^{2}+ \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}},y \left ( x \right ) ={\frac {1}{8\,{\it \_C1}} \left ( 11\,i\sqrt {3}{{\it \_C1}}^{2}{x}^{2}+i\sqrt {3} \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}}+11\,{{\it \_C1}}^{2}{x}^{2}-2\,{\it \_C1}\,x\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}- \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}} \right \} \]