ODE No. 762

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

✓ Mathematica : cpu = 0.124595 (sec), leaf count = 26

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

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

✓ Maple : cpu = 0.137 (sec), leaf count = 22

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

\[y \left (x \right ) = \left (1+x \right )^{-\frac {1}{x}} {\mathrm e} \,{\mathrm e}^{\frac {c_{1}}{x}}\]