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]