##### 4.9.50 $$(-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0$$

ODE
$(-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0$ 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 = 0.204707 (sec), leaf count = 30

$\left \{\left \{y(x)\to -\frac {3}{5} W\left (-e^{\frac {25 x}{3}-1+c_1}\right )+2 x+\frac {7}{5}\right \}\right \}$

Maple
cpu = 0.095 (sec), leaf count = 21

$\left [y \left (x \right ) = 2 x -\frac {3 \LambertW \left (-\frac {{\mathrm e}^{\frac {25 x}{3}} {\mathrm e}^{\frac {7}{3}} \textit {\_C1}}{3}\right )}{5}+\frac {7}{5}\right ]$ Mathematica raw input

DSolve[3*(1 + 2*x - y[x]) + (2 + 2*x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> 7/5 + 2*x - (3*ProductLog[-E^(-1 + (25*x)/3 + C[1])])/5}}

Maple raw input

dsolve((2+2*x-y(x))*diff(y(x),x)+3+6*x-3*y(x) = 0, y(x))

Maple raw output

[y(x) = 2*x-3/5*LambertW(-1/3*exp(25/3*x)*exp(7/3)*_C1)+7/5]