##### 4.13.49 $$x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0$$

ODE
$x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0$ ODE Classiﬁcation

[[_homogeneous, class A], _rational, _dAlembert]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.361989 (sec), leaf count = 26

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

Maple
cpu = 0.094 (sec), leaf count = 22

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = tan(RootOf(ln(tan(_Z))-_Z+2*ln(x)+2*_C1))*x]