#### 2.305   ODE No. 305

$x^2+\left (y(x)^3-3 x\right ) y'(x)-3 y(x)=0$ Mathematica : cpu = 0.180427 (sec), leaf count = 1277

$\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}-\frac {1}{2} \sqrt {-\frac {24 x}{\sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}}-\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}-\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {-\frac {24 x}{\sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}}-\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}-\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}-\frac {1}{2} \sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}-\frac {1}{2} \sqrt {\frac {24 x}{\sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}}-\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}-\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}+\frac {1}{2} \sqrt {\frac {24 x}{\sqrt {\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}+\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}}}-\frac {\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}{9 \sqrt [3]{2}}-\frac {16 \sqrt [3]{2} \left (x^3+3 c_1\right )}{\sqrt [3]{104976 x^2-\sqrt {11019960576 x^4-4 \left (144 x^3+432 c_1\right ){}^3}}}}\right \}\right \}$ Maple : cpu = 0.015 (sec), leaf count = 21

$\left \{ {\frac {{x}^{3}}{3}}-3\,xy \left ( x \right ) +{\frac { \left ( y \left ( x \right ) \right ) ^{4}}{4}}+{\it \_C1}=0 \right \}$