##### 4.10.32 $$(-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0$$

ODE
$(-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0$ 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 = 0.177136 (sec), leaf count = 30

$\left \{\left \{y(x)\to \frac {1}{6} \left (-3 W\left (-e^{\frac {4 x}{3}-1+c_1}\right )-2 x+5\right )\right \}\right \}$

Maple
cpu = 0.093 (sec), leaf count = 21

$\left [y \left (x \right ) = -\frac {x}{3}-\frac {\LambertW \left (-\frac {{\mathrm e}^{\frac {4 x}{3}} {\mathrm e}^{\frac {5}{3}} \textit {\_C1}}{3}\right )}{2}+\frac {5}{6}\right ]$ Mathematica raw input

DSolve[3 - x - 3*y[x] + (4 - x - 3*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (5 - 2*x - 3*ProductLog[-E^(-1 + (4*x)/3 + C[1])])/6}}

Maple raw input

dsolve((4-x-3*y(x))*diff(y(x),x)+3-x-3*y(x) = 0, y(x))

Maple raw output

[y(x) = -1/3*x-1/2*LambertW(-1/3*exp(4/3*x)*exp(5/3)*_C1)+5/6]