\[ y'(x)=\frac {y(x) (y(x)+x+1)}{(x+1) \left (2 y(x)^3+y(x)+x\right )} \] ✓ Mathematica : cpu = 0.527223 (sec), leaf count = 27
DSolve[Derivative[1][y][x] == (y[x]*(1 + x + y[x]))/((1 + x)*(x + y[x] + 2*y[x]^3)),y[x],x]
\[\text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))-\log (x+1)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.187 (sec), leaf count = 30
dsolve(diff(y(x),x) = 1/(2*y(x)^3+y(x)+x)*(x+y(x)+1)*y(x)/(1+x),y(x))
\[y \left (x \right ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{3 \textit {\_Z}}+\ln \left (1+x \right ) {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} c_{1}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )}\]