2.343   ODE No. 343

\[ y'(x) (\log (y(x))+x)-1=0 \]

✓ Mathematica : cpu = 0.206343 (sec), leaf count = 35

DSolve[-1 + (x + Log[y[x]])*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [x=e^{y(x)} \left (\text {Ei}(-y(x))-e^{-y(x)} \log (y(x))\right )+c_1 e^{y(x)},y(x)\right ]\]

✓ Maple : cpu = 0.062 (sec), leaf count = 27

dsolve((ln(y(x))+x)*diff(y(x),x)-1 = 0,y(x))
 

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