4.10.35 \((-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0\)

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 = 0.0179894 (sec), leaf count = 26

\[\left \{\left \{y(x)\to \frac {1}{6} \left (W\left (-e^{c_1-20 x-1}\right )+18 x+3\right )\right \}\right \}\]

Maple
cpu = 0.025 (sec), leaf count = 26

\[ \left \{ {\frac {x}{10}}+{\frac {\ln \left (2\,y \relax (x ) -6\,x-1 \right ) }{20}}+{\frac {3\,y \relax (x ) }{10}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/10*x+1/20*ln(2*y(x)-6*x-1)+3/10*y(x)-_C1 = 0