##### 4.10.36 $$(4 y(x)+x) y'(x)-y(x)+4 x=0$$

ODE
$(4 y(x)+x) y'(x)-y(x)+4 x=0$ 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 = 0.210276 (sec), leaf count = 31

$\text {Solve}\left [2 \log \left (\frac {y(x)^2}{x^2}+1\right )+\tan ^{-1}\left (\frac {y(x)}{x}\right )+4 \log (x)=c_1,y(x)\right ]$

Maple
cpu = 0.134 (sec), leaf count = 24

$\left [y \left (x \right ) = \tan \left (\RootOf \left (2 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+\textit {\_Z} +4 \ln \left (x \right )+4 \textit {\_C1} \right )\right ) x\right ]$ Mathematica raw input

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

Mathematica raw output

Solve[ArcTan[y[x]/x] + 4*Log[x] + 2*Log[1 + y[x]^2/x^2] == C[1], y[x]]

Maple raw input

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

Maple raw output

[y(x) = tan(RootOf(2*ln(1/cos(_Z)^2)+_Z+4*ln(x)+4*_C1))*x]