4.10.30 $3(2-y(x))y^{\prime }(x)+xy(x)=0$

ODE
$$3(2-y(x))y^{\prime }(x)+xy(x)=0$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.0301078 (sec), leaf count = 59

$$\{\{y(x)\to -2W(-\frac{1}{2}\sqrt{e^{-c_1-\frac{x^2}{6}}})\},\{y(x)\to -2W\left(\frac{1}{2}\sqrt{e^{-c_1-\frac{x^2}{6}}}\right)\}\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 19

$$\{\frac{x^2}{2}-3y\left(x\right)+6\ln \left(y\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[x*y[x] + 3*(2 - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -2*ProductLog[-Sqrt[E^(-x^2/6 - C[1])]/2]}, {y[x] -> -2*ProductLog[Sqr
t[E^(-x^2/6 - C[1])]/2]}}

Maple raw input

dsolve(3*(2-y(x))*diff(y(x),x)+x*y(x) = 0, y(x),'implicit')

Maple raw output

1/2*x^2-3*y(x)+6*ln(y(x))+_C1 = 0