ODE
\[ 3 (2 y(x)+x) y'(x)=-2 y(x)-x+1 \] ODE Classification
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 0.171911 (sec), leaf count = 28
\[\left \{\left \{y(x)\to -W\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1\right \}\right \}\]
Maple ✓
cpu = 0.109 (sec), leaf count = 33
\[\left [y \left (x \right ) = {\mathrm e}^{-\LambertW \left (-{\mathrm e}^{-1} {\mathrm e}^{-\frac {x}{6}} {\mathrm e}^{\frac {\textit {\_C1}}{6}}\right )-1-\frac {x}{6}+\frac {\textit {\_C1}}{6}}-1-\frac {x}{2}\right ]\] Mathematica raw input
DSolve[3*(x + 2*y[x])*y'[x] == 1 - x - 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -1 - x/2 - ProductLog[-E^(-1 - x/6 + C[1])]}}
Maple raw input
dsolve(3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x), y(x))
Maple raw output
[y(x) = exp(-LambertW(-exp(-1)*exp(-1/6*x)*exp(1/6*_C1))-1-1/6*x+1/6*_C1)-1-1/2*x]