##### 4.10.39 $$(-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2$$

ODE
$(-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2$ 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 = 0.181201 (sec), leaf count = 71

$\left \{\left \{y(x)\to \frac {1}{4} \left (-i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right )\right \}\right \}$

Maple
cpu = 0.191 (sec), leaf count = 38

$\left [y \left (x \right ) = \frac {29}{19}-\frac {-\frac {3 \left (-7+19 x \right ) \textit {\_C1}}{2}+\frac {\sqrt {-19 \left (-7+19 x \right )^{2} \textit {\_C1}^{2}+4}}{2}}{38 \textit {\_C1}}\right ]$ Mathematica raw input

DSolve[(5 + 3*x - 4*y[x])*y'[x] == 2 + 7*x - 3*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (5 + 3*x - I*Sqrt[-25 - 14*x + 19*x^2 - 16*C[1]])/4}, {y[x] -> (5 + 3*
x + I*Sqrt[-25 - 14*x + 19*x^2 - 16*C[1]])/4}}

Maple raw input

dsolve((5+3*x-4*y(x))*diff(y(x),x) = 2+7*x-3*y(x), y(x))

Maple raw output

[y(x) = 29/19-1/38*(-3/2*(-7+19*x)*_C1+1/2*(-19*(-7+19*x)^2*_C1^2+4)^(1/2))/_C1]