\[ y'(x)=\frac {y(x) \left (3 x y(x)^2+3 y(x)^2+x\right )}{x (x+1) \left (6 y(x)^2+x\right )} \] ✓ Mathematica : cpu = 0.580116 (sec), leaf count = 70
\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \}\right \}\] ✓ Maple : cpu = 0.426 (sec), leaf count = 51
\[\left \{\frac {1}{\frac {6}{x}+\frac {1}{y \left (x \right )^{2}}} = \frac {\left ({\mathrm e}^{\RootOf \left (3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {\left (x +1\right )^{2} \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{2 x}\right )+9\right )}+9\right ) x}{54}\right \}\]