4.10.46 \(3 (2 y(x)+x) y'(x)=-2 y(x)-x+1\)

ODE
\[ 3 (2 y(x)+x) y'(x)=-2 y(x)-x+1 \] 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 = 0.0184854 (sec), leaf count = 28

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

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

\[ \left \{ -{\it \_C1}-x-3\,y \relax (x ) +3\,\ln \left (1+x/2+y \relax (x ) \right ) =0 \right \} \] 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