4.12.25 $x^2(1-y(x))y^{\prime }(x)+(x+1)y(x{)}^2=0$

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.0184982 (sec), leaf count = 25

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

Maple ✓
cpu = 0.011 (sec), leaf count = 23

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

-1/x+ln(x)-1/y(x)-ln(y(x))+_C1 = 0