4.12.47 $y(x{)}^2{y}^{\prime }(x)+x(2-y(x))=0$

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 26.9186 (sec), leaf count = 38

$$\left\{\{y(x)\to \text{InverseFunction}[\frac{{\mathrm{\#}\text{1}}^2}{2}+2\mathrm{\#}\text{1}+4\log (\mathrm{\#}\text{1}-2)-6\mathrm{\&}][c_1+\frac{x^2}{2}]\}\right\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 27

$$\{\frac{x^2}{2}-\frac{{\left(y\left(x\right)\right)}^2}{2}-2y\left(x\right)-4\ln (y\left(x\right)-2)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> InverseFunction[-6 + 4*Log[-2 + #1] + 2*#1 + #1^2/2 & ][x^2/2 + C[1]]}
}

Maple raw input

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

Maple raw output

1/2*x^2-1/2*y(x)^2-2*y(x)-4*ln(y(x)-2)+_C1 = 0