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 = 0.167262 (sec), leaf count = 402


\[\left \{\left \{y(x)\to \frac {\sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{12 \sqrt [3]{2}}-\frac {33 x^2}{2\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}-\frac {x}{4}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{24 \sqrt [3]{2}}+\frac {33 \left (1+i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}-\frac {x}{4}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}{24 \sqrt [3]{2}}+\frac {33 \left (1-i \sqrt {3}\right ) x^2}{4\ 2^{2/3} \sqrt [3]{54 x^3+\sqrt {3881196 x^6+\left (54 x^3+432 e^{3 c_1}\right ){}^2}+432 e^{3 c_1}}}-\frac {x}{4}\right \}\right \}\] Maple : cpu = 0.077 (sec), leaf count = 432


\[y \relax (x ) = \frac {\frac {\left (x^{3} c_{1}^{3}+8+2 \sqrt {333 x^{6} c_{1}^{6}+4 x^{3} c_{1}^{3}+16}\right )^{\frac {1}{3}}}{4}-\frac {11 c_{1}^{2} x^{2}}{4 \left (x^{3} c_{1}^{3}+8+2 \sqrt {333 x^{6} c_{1}^{6}+4 x^{3} c_{1}^{3}+16}\right )^{\frac {1}{3}}}-\frac {c_{1} x}{4}}{c_{1}}\]