2.750   ODE No. 750

\[ y'(x)=\frac {y(x) \left (x^2+3 y(x)^2\right )}{x \left (6 y(x)^2+x\right )} \] Mathematica : cpu = 0.28709 (sec), leaf count = 72


\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 x+2 c_1}}{x}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 x+2 c_1}}{x}\right )}}{\sqrt {6}}\right \}\right \}\] Maple : cpu = 0.432 (sec), leaf count = 49


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