ODE
\[ x y'(x)=x e^{\frac {y(x)}{x}}+y(x) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.307115 (sec), leaf count = 18
\[\{\{y(x)\to -x \log (-\log (x)-c_1)\}\}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 15
\[\left [y \left (x \right ) = \ln \left (-\frac {1}{\ln \left (x \right )+\textit {\_C1}}\right ) x\right ]\] Mathematica raw input
DSolve[x*y'[x] == E^(y[x]/x)*x + y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(x*Log[-C[1] - Log[x]])}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)+x*exp(y(x)/x), y(x))
Maple raw output
[y(x) = ln(-1/(ln(x)+_C1))*x]