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

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 = 0.0177299 (sec), leaf count = 30

\[\left \{\left \{y(x)\to -\frac {3}{5} W\left (-e^{c_1+\frac {25 x}{3}-1}\right )+2 x+\frac {7}{5}\right \}\right \}\]

Maple
cpu = 0.026 (sec), leaf count = 26

\[ \left \{ {\frac {3\,x}{5}}-{\frac {3\,\ln \left (5\,y \relax (x ) -10\,x-7 \right ) }{25}}+{\frac {y \relax (x ) }{5}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

3/5*x-3/25*ln(5*y(x)-10*x-7)+1/5*y(x)-_C1 = 0