4.10.33 \((3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1\)

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

\[ \left \{ -{\it \_C1}+x+3\,\ln \left (3\,y \relax (x ) +2\,x-7 \right ) +y \relax (x ) =0 \right \} \] 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