##### 4.10.38 $$(-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3$$

ODE
$(-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3$ 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 = 0.176434 (sec), leaf count = 61

$\left \{\left \{y(x)\to \frac {1}{4} \left (2 x-i \sqrt {4 x-25-16 c_1}+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (2 x+i \sqrt {4 x-25-16 c_1}+5\right )\right \}\right \}$

Maple
cpu = 0.029 (sec), leaf count = 41

$\left [y \left (x \right ) = \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 \textit {\_C1} -4 x +25}}{4}, y \left (x \right ) = \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 \textit {\_C1} -4 x +25}}{4}\right ]$ Mathematica raw input

DSolve[(5 + 2*x - 4*y[x])*y'[x] == 3 + x - 2*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (5 + 2*x - I*Sqrt[-25 + 4*x - 16*C[1]])/4}, {y[x] -> (5 + 2*x + I*Sqrt
[-25 + 4*x - 16*C[1]])/4}}

Maple raw input

dsolve((5+2*x-4*y(x))*diff(y(x),x) = 3+x-2*y(x), y(x))

Maple raw output

[y(x) = 1/2*x+5/4-1/4*(4*_C1-4*x+25)^(1/2), y(x) = 1/2*x+5/4+1/4*(4*_C1-4*x+25)^
(1/2)]