##### 4.10.24 $$(6 x-2 y(x)) y'(x)=-y(x)+3 x+2$$

ODE
$(6 x-2 y(x)) y'(x)=-y(x)+3 x+2$ 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 = 0.173603 (sec), leaf count = 29

$\left \{\left \{y(x)\to 3 x-\frac {2}{5} \left (1+W\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right )\right \}\right \}$

Maple
cpu = 0.111 (sec), leaf count = 35

$\left [y \left (x \right ) = \frac {{\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{\frac {25 x}{4}} {\mathrm e}^{-1} {\mathrm e}^{-\frac {25 \textit {\_C1}}{4}}}{2}\right )+\frac {25 x}{4}-1-\frac {25 \textit {\_C1}}{4}}}{5}+3 x -\frac {2}{5}\right ]$ Mathematica raw input

DSolve[(6*x - 2*y[x])*y'[x] == 2 + 3*x - y[x],y[x],x]

Mathematica raw output

{{y[x] -> 3*x - (2*(1 + ProductLog[-E^(-1 + (25*x)/4 + C[1])]))/5}}

Maple raw input

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

Maple raw output

[y(x) = 1/5*exp(-LambertW(-1/2*exp(25/4*x)*exp(-1)*exp(-25/4*_C1))+25/4*x-1-25/4
*_C1)+3*x-2/5]