4.10.46 $3(2y(x)+x)y^{\prime }(x)=-2y(x)-x+1$

ODE
$$3(2y(x)+x)y^{\prime }(x)=-2y(x)-x+1$$ ODE Classification

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Book solution method
Equation linear in the variables, $y^{\prime }(x)=f\left(\frac{X_1}{X_2}\right)$

Mathematica ✓
cpu = 0.0184854 (sec), leaf count = 28

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

Maple ✓
cpu = 0.022 (sec), leaf count = 24

$$\{-\mathit{\_}\mathit{C}\mathit{1}-x-3y\left(x\right)+3\ln (1+x/2+y\left(x\right))=0\}$$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x), y(x),'implicit')

Maple raw output

-_C1-x-3*y(x)+3*ln(1+1/2*x+y(x)) = 0