4.10.1 \((-y(x)+2 x+3) y'(x)+2=0\)

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 = 0.0198444 (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 = 0.025 (sec), leaf count = 18

\[ \left \{ x-{\frac {y \relax (x ) }{2}}+2-{{\rm e}^{-y \relax (x ) }}{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

x-1/2*y(x)+2-exp(-y(x))*_C1 = 0