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 = 0.0135442 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -x \log \left (-c_1-\log (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 18
\[ \left \{ -{\it \_C1}+ \left ( {{\rm e}^{{\frac {y \left ( x \right ) }{x}}}} \right ) ^{-1}+\ln \left ( x \right ) =0 \right \} \] 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),'implicit')
Maple raw output
-_C1+1/exp(y(x)/x)+ln(x) = 0