ODE
\[ (3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1 \] 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 = 0.173696 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{3} \left (9 W\left (-e^{-\frac {x}{9}-1+c_1}\right )-2 x+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.094 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\frac {2 x}{3}+3 \LambertW \left (\frac {{\mathrm e}^{-\frac {x}{9}} \textit {\_C1} \,{\mathrm e}^{-\frac {7}{9}}}{9}\right )+\frac {7}{3}\right ]\] Mathematica raw input
DSolve[(2 + 2*x + 3*y[x])*y'[x] == 1 - 2*x - 3*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (7 - 2*x + 9*ProductLog[-E^(-1 - x/9 + C[1])])/3}}
Maple raw input
dsolve((2+2*x+3*y(x))*diff(y(x),x) = 1-2*x-3*y(x), y(x))
Maple raw output
[y(x) = -2/3*x+3*LambertW(1/9*exp(-1/9*x)*_C1*exp(-7/9))+7/3]