4.18.50 $x^2{y}^{\prime }(x{)}^2-x{y}^{\prime }(x)+(1-y(x))y(x)=0$

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

[_separable]

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.0045838 (sec), leaf count = 21

$$\{\{y(x)\to c_{1}x\},\{y(x)\to \frac{c_1+x}{x}\}\}$$

Maple ✓
cpu = 0.01 (sec), leaf count = 17

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x,y\left(x\right)=\frac{x+\mathit{\_}\mathit{C}\mathit{1}}{x}\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> x*C[1]}, {y[x] -> (x + C[1])/x}}

Maple raw input

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

Maple raw output

y(x) = _C1*x, y(x) = (x+_C1)/x