##### 4.10.6 $$(4 x-y(x)) y'(x)-5 y(x)+2 x=0$$

ODE
$(4 x-y(x)) y'(x)-5 y(x)+2 x=0$ ODE Classiﬁcation

[[_homogeneous, class A], _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 = 0.186203 (sec), leaf count = 80

$\left \{\left \{y(x)\to \frac {1}{2} \left (-4 x-e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-4 x+e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right )\right \}\right \}$

Maple
cpu = 0.048 (sec), leaf count = 47

$\left [y \left (x \right ) = -\frac {4 x \textit {\_C1} -\sqrt {-12 x \textit {\_C1} +1}-1}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {4 x \textit {\_C1} +\sqrt {-12 x \textit {\_C1} +1}-1}{2 \textit {\_C1}}\right ]$ Mathematica raw input

DSolve[2*x - 5*y[x] + (4*x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-E^C[1] - 4*x - E^(C[1]/2)*Sqrt[E^C[1] + 12*x])/2}, {y[x] -> (-E^C[1]
 - 4*x + E^(C[1]/2)*Sqrt[E^C[1] + 12*x])/2}}

Maple raw input

dsolve((4*x-y(x))*diff(y(x),x)+2*x-5*y(x) = 0, y(x))

Maple raw output

[y(x) = -1/2*(4*x*_C1-(-12*_C1*x+1)^(1/2)-1)/_C1, y(x) = -1/2*(4*x*_C1+(-12*_C1*
x+1)^(1/2)-1)/_C1]