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 = 0.0197388 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{3} \left (9 W\left (-e^{c_1-\frac {x}{9}-1}\right )-2 x+7\right )\right \}\right \}\]
Maple ✓
cpu = 0.028 (sec), leaf count = 22
\[ \left \{ -{\it \_C1}+x+3\,\ln \left ( 3\,y \left ( x \right ) +2\,x-7 \right ) +y \left ( x \right ) =0 \right \} \] 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),'implicit')
Maple raw output
-_C1+x+3*ln(3*y(x)+2*x-7)+y(x) = 0