4.12.23 $x(3-xy(x))y^{\prime }(x)=y(x)(xy(x)-1)$

ODE
$$x(3-xy(x))y^{\prime }(x)=y(x)(xy(x)-1)$$ ODE Classification

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

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 4.95322 (sec), leaf count = 30

$$\left\{\{y(x)\to -\frac{3W\left(e^{\frac{9c_1}{2^{2/3}}-1}{x}^{2/3}\right)}{x}\}\right\}$$

Maple ✓
cpu = 0.011 (sec), leaf count = 21

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

DSolve[x*(3 - x*y[x])*y'[x] == y[x]*(-1 + x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> (-3*ProductLog[E^(-1 + (9*C[1])/2^(2/3))*x^(2/3)])/x}}

Maple raw input

dsolve(x*(3-x*y(x))*diff(y(x),x) = y(x)*(x*y(x)-1), y(x),'implicit')

Maple raw output

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