4.5.20 $x{y}^{\prime }(x)+y(x)(-\log (y(x))-\log (x)+1)=0$

ODE
$$x{y}^{\prime }(x)+y(x)(-\log (y(x))-\log (x)+1)=0$$ ODE Classification

[[_homogeneous, `class G`]]

Book solution method
Change of Variable, new dependent variable

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

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

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

$$\{\frac{-\mathit{\_}\mathit{C}\mathit{1}x+\ln \left(x\right)+\ln \left(y\left(x\right)\right)}{x}=0\}$$ 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