4.472   (− 2y(x) + 2x+ 3)y′(x) = − 2y(x )+ 6x+ 1

ODE

(− 2y(x)+ 2x+ 3)y′(x) = − 2y(x)+ 6x+ 1

ODE Classification

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Book solution method
Equation linear in the variables,         (  )
y′(x) = f X1
         X2

Mathematica
cpu = 0.00981036 (sec), leaf count = 67

{ {        1 ∘ -----------------      3}  {       1 ∘ -----------------      3}}
   y(x) → −2 i − 4c1 + 8x2 − 8x− 9 +x + 2 , y(x) → 2i  − 4c1 + 8x2 − 8x − 9+ x + 2

Maple
cpu = 0.02 (sec), leaf count = 50

{      (                                       )                      }
   1    4 (y (x))2 + (− 8x − 12)y(x)+ 12x2 + 4x +11
 − 2 ln  ---------------(− 1+-2x)2--------------  − ln(− 1+ 2x)−-C1 = 0

Mathematica raw input

DSolve[(3 + 2*x - 2*y[x])*y'[x] == 1 + 6*x - 2*y[x],y[x],x]

Mathematica raw output

{{y[x] -> 3/2 + x - (I/2)*Sqrt[-9 - 8*x + 8*x^2 - 4*C[1]]}, {y[x] -> 3/2 + x + (
I/2)*Sqrt[-9 - 8*x + 8*x^2 - 4*C[1]]}}

Maple raw input

dsolve((3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x), y(x),'implicit')

Maple raw output

-1/2*ln((4*y(x)^2+(-8*x-12)*y(x)+12*x^2+4*x+11)/(-1+2*x)^2)-ln(-1+2*x)-_C1 = 0