4.10.5 $(y(x)-3x+2)y^{\prime }(x)-3y(x)-2x+5=0$

ODE
$$(y(x)-3x+2)y^{\prime }(x)-3y(x)-2x+5=0$$ ODE Classification

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

Book solution method
Equation linear in the variables, $y^{\prime }(x)=f\left(\frac{X_1}{X_2}\right)$

Mathematica ✓
cpu = 0.0118295 (sec), leaf count = 63

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

Maple ✓
cpu = 0.02 (sec), leaf count = 44

$$\{-\frac{1}{2}\ln \left(\frac{{\left(y\left(x\right)\right)}^2+(-6x+4)y\left(x\right)-2x^2+10x-7}{{(-1+x)}^2}\right)-\ln (-1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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),'implicit')

Maple raw output

-1/2*ln((y(x)^2+(-6*x+4)*y(x)-2*x^2+10*x-7)/(-1+x)^2)-ln(-1+x)-_C1 = 0