2.341   ODE No. 341

\[ \left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0 \]

✓ Mathematica : cpu = 0.349192 (sec), leaf count = 33

DSolve[E^y[x] + E^x*y[x] + (E^x + E^y[x]*x)*Derivative[1][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.052 (sec), leaf count = 33

dsolve((x*exp(y(x))+exp(x))*diff(y(x),x)+exp(y(x))+y(x)*exp(x) = 0,y(x))
 

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