ODE No. 711

\[ y'(x)=\frac {y(x) (-x \log (y(x))-\log (y(x))+1)}{x+1} \]

✓ Mathematica : cpu = 0.177246 (sec), leaf count = 28

DSolve[Derivative[1][y][x] == ((1 - Log[y[x]] - x*Log[y[x]])*y[x])/(1 + x),y[x],x]

\[\left \{\left \{y(x)\to e^{e^{-x-1} \text {Ei}(x+1)+c_1 e^{-x}}\right \}\right \}\]

✓ Maple : cpu = 0.203 (sec), leaf count = 31

dsolve(diff(y(x),x) = -(ln(y(x))*x+ln(y(x))-1)*y(x)/(1+x),y(x))

\[y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{-x} c_{1}} {\mathrm e}^{-\operatorname {Ei}_{1}\left (-1-x \right ) {\mathrm e}^{-1-x}}\]