ODE
\[ (-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0 \] 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 = 0.182864 (sec), leaf count = 30
\[\left \{\left \{y(x)\to -4 W\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3}\right \}\right \}\]
Maple ✓
cpu = 0.09 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\frac {2 x}{3}-4 \LambertW \left (-\frac {{\mathrm e}^{\frac {x}{12}} \textit {\_C1} \,{\mathrm e}^{-\frac {7}{12}}}{12}\right )-\frac {7}{3}\right ]\] Mathematica raw input
DSolve[1 - 2*x - 3*y[x] + (5 - 2*x - 3*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -7/3 - (2*x)/3 - 4*ProductLog[-E^(-1 + x/12 + C[1])]}}
Maple raw input
dsolve((5-2*x-3*y(x))*diff(y(x),x)+1-2*x-3*y(x) = 0, y(x))
Maple raw output
[y(x) = -2/3*x-4*LambertW(-1/12*exp(1/12*x)*_C1*exp(-7/12))-7/3]