4.5.20 \(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\)

ODE
\[ x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0 \] ODE Classification

[[_homogeneous, `class G`]]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.0297898 (sec), leaf count = 19

\[\left \{\left \{y(x)\to \frac {e^{e^{-c_1} x}}{x}\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 17

\[ \left \{ {\frac {-{\it \_C1}\,x+\ln \relax (x ) +\ln \left (y \relax (x ) \right ) }{x}}=0 \right \} \] Mathematica raw input

DSolve[(1 - Log[x] - Log[y[x]])*y[x] + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(x/E^C[1])/x}}

Maple raw input

dsolve(x*diff(y(x),x)+(1-ln(x)-ln(y(x)))*y(x) = 0, y(x),'implicit')

Maple raw output

(-_C1*x+ln(x)+ln(y(x)))/x = 0