\[ y'(x)=\frac {y(x) \left (3 x y(x)^2+3 y(x)^2+x\right )}{x (x+1) \left (6 y(x)^2+x\right )} \] ✓ Mathematica : cpu = 0.474483 (sec), leaf count = 70
DSolve[Derivative[1][y][x] == (y[x]*(x + 3*y[x]^2 + 3*x*y[x]^2))/(x*(1 + x)*(x + 6*y[x]^2)),y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \}\right \}\] ✓ Maple : cpu = 0.377 (sec), leaf count = 51
dsolve(diff(y(x),x) = 1/(6*y(x)^2+x)*(3*x*y(x)^2+x+3*y(x)^2)*y(x)/x/(1+x),y(x))
\[\frac {1}{\frac {1}{y \left (x \right )^{2}}+\frac {6}{x}} = \frac {\left ({\mathrm e}^{\RootOf \left (-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {\left (1+x \right )^{2} \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{2 x}\right )+3 \,{\mathrm e}^{\textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54}\]