##### 4.10.5 $$(y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0$$

ODE
$(y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0$ 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 = 0.160133 (sec), leaf count = 63

$\left \{\left \{y(x)\to -i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2\right \},\left \{y(x)\to i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2\right \}\right \}$

Maple
cpu = 0.183 (sec), leaf count = 32

$\left [y \left (x \right ) = 1-\frac {-3 \textit {\_C1} \left (x -1\right )+\sqrt {11 \left (x -1\right )^{2} \textit {\_C1}^{2}+1}}{\textit {\_C1}}\right ]$ Mathematica raw input

DSolve[5 - 2*x - 3*y[x] + (2 - 3*x + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -2 + 3*x - I*Sqrt[-4 + 22*x - 11*x^2 - C[1]]}, {y[x] -> -2 + 3*x + I*S
qrt[-4 + 22*x - 11*x^2 - C[1]]}}

Maple raw input

dsolve((2-3*x+y(x))*diff(y(x),x)+5-2*x-3*y(x) = 0, y(x))

Maple raw output

[y(x) = 1-(-3*_C1*(x-1)+(11*(x-1)^2*_C1^2+1)^(1/2))/_C1]