4.13.49 $x(x^2-xy(x)+y(x{)}^2)y^{\prime }(x)+y(x)(x^2+xy(x)+y(x{)}^2)=0$

ODE
$$x(x^2-xy(x)+y(x{)}^2)y^{\prime }(x)+y(x)(x^2+xy(x)+y(x{)}^2)=0$$ ODE Classification

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

Book solution method
Homogeneous equation

Mathematica ✓
cpu = 0.0363929 (sec), leaf count = 26

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

Maple ✓
cpu = 0.018 (sec), leaf count = 29

$$\{\frac{1}{2}\arctan \left(\frac{y\left(x\right)}{x}\right)-\frac{1}{2}\ln \left(\frac{y\left(x\right)}{x}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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),'implicit')

Maple raw output

1/2*arctan(y(x)/x)-1/2*ln(y(x)/x)-ln(x)-_C1 = 0