ODE
\[ x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.333613 (sec), leaf count = 21
\[\left \{\left \{y(x)\to -x \log \left (-1+\frac {e^{-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.115 (sec), leaf count = 20
\[\left [y \left (x \right ) = \left (\ln \left (-\frac {x}{-1+x \,{\mathrm e}^{\textit {\_C1}}}\right )+\textit {\_C1} \right ) x\right ]\] Mathematica raw input
DSolve[x*y'[x] == x + E^(y[x]/x)*x + y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x*Log[-1 + 1/(E^C[1]*x)])}}
Maple raw input
dsolve(x*diff(y(x),x) = x+y(x)+x*exp(y(x)/x), y(x))
Maple raw output
[y(x) = (ln(-x/(-1+x*exp(_C1)))+_C1)*x]