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 = 0.0166686 (sec), leaf count = 30

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

Maple
cpu = 0.027 (sec), leaf count = 26

\[ \left \{ {\frac {3\,x}{2}}-{\frac {3\,\ln \left (6\,y \relax (x ) +2\,x-5 \right ) }{4}}+{\frac {3\,y \relax (x ) }{2}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

3/2*x-3/4*ln(6*y(x)+2*x-5)+3/2*y(x)-_C1 = 0