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 = 0.0184854 (sec), leaf count = 28
\[\left \{\left \{y(x)\to -W\left (-e^{c_1-\frac {x}{6}-1}\right )-\frac {x}{2}-1\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 24
\[ \left \{ -{\it \_C1}-x-3\,y \left ( x \right ) +3\,\ln \left ( 1+x/2+y \left ( x \right ) \right ) =0 \right \} \] 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),'implicit')
Maple raw output
-_C1-x-3*y(x)+3*ln(1+1/2*x+y(x)) = 0