ODE
\[ (x-y(x)) y'(x)=\left (e^{-\frac {x}{y(x)}}+1\right ) y(x) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.462823 (sec), leaf count = 23
\[\left \{\left \{y(x)\to -\frac {x}{W\left (\frac {x}{x-e^{c_1}}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.196 (sec), leaf count = 20
\[\left [y \left (x \right ) = -\frac {x}{\LambertW \left (\frac {x \textit {\_C1}}{x \textit {\_C1} -1}\right )}\right ]\] Mathematica raw input
DSolve[(x - y[x])*y'[x] == (1 + E^(-(x/y[x])))*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x/ProductLog[x/(-E^C[1] + x)])}}
Maple raw input
dsolve((x-y(x))*diff(y(x),x) = (exp(-x/y(x))+1)*y(x), y(x))
Maple raw output
[y(x) = -x/LambertW(x*_C1/(_C1*x-1))]