2.781   ODE No. 781

\[ y'(x)=\frac {y(x) \left (x^4+x^3+3 y(x)^2+x\right )}{x \left (6 y(x)^2+x\right )} \] Mathematica : cpu = 0.418494 (sec), leaf count = 82


\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (6 x e^{\frac {2 x^3}{3}+x^2+2 c_1}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (6 x e^{\frac {2 x^3}{3}+x^2+2 c_1}\right )}}{\sqrt {6}}\right \}\right \}\] Maple : cpu = 0.63 (sec), leaf count = 61


\[\frac {1}{\frac {1}{y \relax (x )^{2}}+\frac {6}{x}} = \frac {\left ({\mathrm e}^{\RootOf \left (2 x^{3} {\mathrm e}^{\textit {\_Z}}+3 x^{2} {\mathrm e}^{\textit {\_Z}}-3 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+9}{2 x}\right )+9 c_{1} {\mathrm e}^{\textit {\_Z}}+3 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+27\right )}+9\right ) x}{54}\]