##### 4.10.30 $$3 (2-y(x)) y'(x)+x y(x)=0$$

ODE
$3 (2-y(x)) y'(x)+x y(x)=0$ ODE Classiﬁcation

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.181149 (sec), leaf count = 59

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

Maple
cpu = 0.084 (sec), leaf count = 29

$\left [y \left (x \right ) = {\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {\textit {\_C1}}{6}}}{2}\right )-\frac {x^{2}}{12}-\frac {\textit {\_C1}}{6}}\right ]$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = exp(-LambertW(-1/2*exp(-1/12*x^2-1/6*_C1))-1/12*x^2-1/6*_C1)]