##### 4.10.22 $$(-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1$$

ODE
$(-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1$ ODE Classiﬁcation

[[_homogeneous, class C], _exact, _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 = 0.168058 (sec), leaf count = 67

$\left \{\left \{y(x)\to -\frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2}\right \},\left \{y(x)\to \frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2}\right \}\right \}$

Maple
cpu = 0.18 (sec), leaf count = 36

$\left [y \left (x \right ) = 2-\frac {-\left (-1+2 x \right ) \textit {\_C1} +\sqrt {-2 \left (-1+2 x \right )^{2} \textit {\_C1}^{2}+1}}{2 \textit {\_C1}}\right ]$ 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))

Maple raw output

[y(x) = 2-1/2*(-(-1+2*x)*_C1+(-2*(-1+2*x)^2*_C1^2+1)^(1/2))/_C1]