2.285   ODE No. 285

$\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0$ Mathematica : cpu = 0.1583 (sec), leaf count = 402

$\left \{\left \{y(x)\to -\frac {33 x^2}{2\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}+\frac {\sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{12 \sqrt [3]{2}}-\frac {x}{4}\right \},\left \{y(x)\to \frac {33 \left (1+i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{24 \sqrt [3]{2}}-\frac {x}{4}\right \},\left \{y(x)\to \frac {33 \left (1-i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{24 \sqrt [3]{2}}-\frac {x}{4}\right \}\right \}$ Maple : cpu = 0.064 (sec), leaf count = 432

$\left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {1}{4}\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}-{\frac {11\,{{\it \_C1}}^{2}{x}^{2}}{4}{\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}}-{\frac {{\it \_C1}\,x}{4}} \right ) },y \left ( x \right ) =-{\frac {1}{8\,{\it \_C1}} \left ( 2\,{\it \_C1}\,x\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}+ \left ( 11\,i{{\it \_C1}}^{2}{x}^{2}+i \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}-11\,{{\it \_C1}}^{2}{x}^{2}+ \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}},y \left ( x \right ) ={\frac {1}{8\,{\it \_C1}} \left ( 11\,i\sqrt {3}{{\it \_C1}}^{2}{x}^{2}+i \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}}\sqrt {3}+11\,{{\it \_C1}}^{2}{x}^{2}-2\,{\it \_C1}\,x\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}- \left ( {x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{x}^{3}{{\it \_C1}}^{3}+8+2\,\sqrt {333\,{{\it \_C1}}^{6}{x}^{6}+4\,{x}^{3}{{\it \_C1}}^{3}+16}}}}} \right \}$