\[ y'(x)=\frac {y(x) (-x \log (y(x))-\log (y(x))+1)}{x+1} \] ✓ Mathematica : cpu = 0.172179 (sec), leaf count = 28
DSolve[Derivative[1][y][x] == ((1 - Log[y[x]] - x*Log[y[x]])*y[x])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to e^{e^{-x-1} \operatorname {ExpIntegralEi}(x+1)+c_1 e^{-x}}\right \}\right \}\] ✓ Maple : cpu = 0.215 (sec), leaf count = 31
dsolve(diff(y(x),x) = -(ln(y(x))*x+ln(y(x))-1)*y(x)/(1+x),y(x))
\[y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{-x} c_{1}} {\mathrm e}^{-\operatorname {expIntegral}_{1}\left (-1-x \right ) {\mathrm e}^{-1-x}}\]