##### 4.10.34 $$(-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0$$

ODE
$(-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0$ 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 = 0.182864 (sec), leaf count = 30

$\left \{\left \{y(x)\to -4 W\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3}\right \}\right \}$

Maple
cpu = 0.09 (sec), leaf count = 21

$\left [y \left (x \right ) = -\frac {2 x}{3}-4 \LambertW \left (-\frac {{\mathrm e}^{\frac {x}{12}} \textit {\_C1} \,{\mathrm e}^{-\frac {7}{12}}}{12}\right )-\frac {7}{3}\right ]$ Mathematica raw input

DSolve[1 - 2*x - 3*y[x] + (5 - 2*x - 3*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -7/3 - (2*x)/3 - 4*ProductLog[-E^(-1 + x/12 + C[1])]}}

Maple raw input

dsolve((5-2*x-3*y(x))*diff(y(x),x)+1-2*x-3*y(x) = 0, y(x))

Maple raw output

[y(x) = -2/3*x-4*LambertW(-1/12*exp(1/12*x)*_C1*exp(-7/12))-7/3]