ODE
\[ (-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0 \] 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 = 0.204707 (sec), leaf count = 30
\[\left \{\left \{y(x)\to -\frac {3}{5} W\left (-e^{\frac {25 x}{3}-1+c_1}\right )+2 x+\frac {7}{5}\right \}\right \}\]
Maple ✓
cpu = 0.095 (sec), leaf count = 21
\[\left [y \left (x \right ) = 2 x -\frac {3 \LambertW \left (-\frac {{\mathrm e}^{\frac {25 x}{3}} {\mathrm e}^{\frac {7}{3}} \textit {\_C1}}{3}\right )}{5}+\frac {7}{5}\right ]\] Mathematica raw input
DSolve[3*(1 + 2*x - y[x]) + (2 + 2*x - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 7/5 + 2*x - (3*ProductLog[-E^(-1 + (25*x)/3 + C[1])])/5}}
Maple raw input
dsolve((2+2*x-y(x))*diff(y(x),x)+3+6*x-3*y(x) = 0, y(x))
Maple raw output
[y(x) = 2*x-3/5*LambertW(-1/3*exp(25/3*x)*exp(7/3)*_C1)+7/5]