\[ y'(x)=\frac {2 y(x)+1}{x \left (2 x y(x)^3+x y(x)^2-2\right )} \] ✓ Mathematica : cpu = 0.464685 (sec), leaf count = 47
DSolve[Derivative[1][y][x] == (1 + 2*y[x])/(x*(-2 + x*y[x]^2 + 2*x*y[x]^3)),y[x],x]
\[\text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.31 (sec), leaf count = 42
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x*y(x)^2+2*x*y(x)^3),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\RootOf \left (x \,{\mathrm e}^{3 \textit {\_Z}}-4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 x c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x +3 \,{\mathrm e}^{\textit {\_Z}} x +16\right )}}{2}-\frac {1}{2}\]