\[ y'(x)=\frac {2 y(x)+1}{x \left (2 x y(x)^4+3 x y(x)^3+x y(x)^2+2 x y(x)+x-2\right )} \] ✓ Mathematica : cpu = 0.774063 (sec), leaf count = 53
DSolve[Derivative[1][y][x] == (1 + 2*y[x])/(x*(-2 + x + 2*x*y[x] + x*y[x]^2 + 3*x*y[x]^3 + 2*x*y[x]^4)),y[x],x]
\[\text {Solve}\left [\frac {1}{192} \left (-16 y(x)^3-12 y(x)^2+12 y(x)-54 \log (4 y(x)+2)+7\right )-\frac {1}{2 x (2 y(x)+1)}=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.333 (sec), leaf count = 50
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x+x*y(x)^2+3*x*y(x)^3+2*x*y(x)+2*x*y(x)^4),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\RootOf \left (2 x \,{\mathrm e}^{4 \textit {\_Z}}-3 x \,{\mathrm e}^{3 \textit {\_Z}}-6 x \,{\mathrm e}^{2 \textit {\_Z}}+48 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+54 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+7 \,{\mathrm e}^{\textit {\_Z}} x +96\right )}}{2}-\frac {1}{2}\]