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 = 0.014644 (sec), leaf count = 17
\[\left \{\left \{y(x)\to x e^{\frac {e^{c_1}}{x}}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 17
\[ \left \{ x\ln \left ( x \right ) -x\ln \left ( y \left ( x \right ) \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
x*ln(x)-x*ln(y(x))-_C1 = 0