ODE
\[ (-y(x)+2 x+3) y'(x)+2=0 \] ODE Classification
[[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 0.201273 (sec), leaf count = 22
\[\left \{\left \{y(x)\to W\left (-2 c_1 e^{-2 (x+2)}\right )+2 x+4\right \}\right \}\]
Maple ✓
cpu = 0.034 (sec), leaf count = 19
\[[y \left (x \right ) = \LambertW \left (-2 \textit {\_C1} \,{\mathrm e}^{-2 x -4}\right )+2 x +4]\] Mathematica raw input
DSolve[2 + (3 + 2*x - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 4 + 2*x + ProductLog[(-2*C[1])/E^(2*(2 + x))]}}
Maple raw input
dsolve((3+2*x-y(x))*diff(y(x),x)+2 = 0, y(x))
Maple raw output
[y(x) = LambertW(-2*_C1*exp(-2*x-4))+2*x+4]