\[ y'(x)=\frac {y(x) \left (x^4+3 x y(x)^2+3 y(x)^2\right )}{x (x+1) \left (6 y(x)^2+x\right )} \] ✓ Mathematica : cpu = 0.549935 (sec), leaf count = 90
DSolve[Derivative[1][y][x] == (y[x]*(x^4 + 3*y[x]^2 + 3*x*y[x]^2))/(x*(1 + x)*(x + 6*y[x]^2)),y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 (x+1)^2 e^{x^2-2 x-3+2 c_1}}{x}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 (x+1)^2 e^{x^2-2 x-3+2 c_1}}{x}\right )}}{\sqrt {6}}\right \}\right \}\] ✓ Maple : cpu = 0.671 (sec), leaf count = 60
dsolve(diff(y(x),x) = (x^4+3*x*y(x)^2+3*y(x)^2)/(6*y(x)^2+x)*y(x)/x/(1+x),y(x))
\[\frac {1}{\frac {1}{y \left (x \right )^{2}}+\frac {6}{x}} = \frac {\left ({\mathrm e}^{\RootOf \left (x^{2} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {x \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{2 \left (1+x \right )^{2}}\right )+3 \,{\mathrm e}^{\textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +9\right )}+9\right ) x}{54}\]