4.12.2 $x(x-2y(x))y^{\prime }(x)+(2x-y(x))y(x)=0$

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

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

Book solution method
Homogeneous equation

Mathematica ✓
cpu = 0.0228071 (sec), leaf count = 62

$$\{\{y(x)\to \frac{1}{2}(x-\frac{\sqrt{x^3-4e^{c_1}}}{\sqrt{x}})\},\{y(x)\to \frac{1}{2}(\frac{\sqrt{x^3-4e^{c_1}}}{\sqrt{x}}+x)\}\}$$

Maple ✓
cpu = 0.013 (sec), leaf count = 27

$$\{-\frac{1}{3}\ln (-\frac{(x-y\left(x\right))y\left(x\right)}{x^2})-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (x - Sqrt[-4*E^C[1] + x^3]/Sqrt[x])/2}, {y[x] -> (x + Sqrt[-4*E^C[1] +
 x^3]/Sqrt[x])/2}}

Maple raw input

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

Maple raw output

-1/3*ln(-y(x)*(x-y(x))/x^2)-ln(x)-_C1 = 0