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 = 0.0301078 (sec), leaf count = 59

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

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

\[ \left \{ {\frac {{x}^{2}}{2}}-3\,y \relax (x ) +6\,\ln \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -2*ProductLog[-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