ODE
\[ x y'(x)=y(x) (-\log (y(x))+\log (x)+1) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.271255 (sec), leaf count = 17
\[\left \{\left \{y(x)\to x e^{\frac {e^{c_1}}{x}}\right \}\right \}\]
Maple ✓
cpu = 0.128 (sec), leaf count = 14
\[\left [y \left (x \right ) = x \,{\mathrm e}^{-\frac {\textit {\_C1}}{x}}\right ]\] Mathematica raw input
DSolve[x*y'[x] == (1 + Log[x] - Log[y[x]])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^(E^C[1]/x)*x}}
Maple raw input
dsolve(x*diff(y(x),x) = (1+ln(x)-ln(y(x)))*y(x), y(x))
Maple raw output
[y(x) = x/exp(1/x*_C1)]