4.12.24 $x^2(1-y(x))y^{\prime }(x)+(1-x)y(x)=0$

ODE
$$x^2(1-y(x))y^{\prime }(x)+(1-x)y(x)=0$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.0167342 (sec), leaf count = 21

$$\left\{\{y(x)\to -W\left(x(-e^{\frac{1}{x}-c_1})\right)\}\right\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 17

$$\{x^{-1}+\ln \left(x\right)+y\left(x\right)-\ln \left(y\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[(1 - x)*y[x] + x^2*(1 - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -ProductLog[-(E^(x^(-1) - C[1])*x)]}}

Maple raw input

dsolve(x^2*(1-y(x))*diff(y(x),x)+(1-x)*y(x) = 0, y(x),'implicit')

Maple raw output

1/x+ln(x)+y(x)-ln(y(x))+_C1 = 0