ODE
\[ (-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0 \] 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 = 0.198414 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {1}{6} \left (W\left (-e^{-20 x-1+c_1}\right )+18 x+3\right )\right \}\right \}\]
Maple ✓
cpu = 0.1 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{-\LambertW \left (3 \,{\mathrm e}^{-20 x} {\mathrm e}^{-3} {\mathrm e}^{20 \textit {\_C1}}\right )-20 x -3+20 \textit {\_C1}}}{2}+3 x +\frac {1}{2}\right ]\] Mathematica raw input
DSolve[2 + 3*x - y[x] + (1 + 9*x - 3*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3 + 18*x + ProductLog[-E^(-1 - 20*x + C[1])])/6}}
Maple raw input
dsolve((1+9*x-3*y(x))*diff(y(x),x)+2+3*x-y(x) = 0, y(x))
Maple raw output
[y(x) = 1/2*exp(-LambertW(3/exp(x)^20*exp(-3)*exp(_C1)^20)-20*x-3+20*_C1)+3*x+1/2]