4.12.10 $x^3+3x(2y(x)+x)y^{\prime }(x)+3y(x)(y(x)+2x)=0$

ODE
$$x^3+3x(2y(x)+x)y^{\prime }(x)+3y(x)(y(x)+2x)=0$$ ODE Classification

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Book solution method
Exact equation

Mathematica ✓
cpu = 0.0110045 (sec), leaf count = 75

$$\{\{y(x)\to -\frac{\sqrt{36c_{1}x-3x^5+9x^4}+3x^2}{6x}\},\{y(x)\to \frac{\sqrt{36c_{1}x-3x^5+9x^4}-3x^2}{6x}\}\}$$

Maple ✓
cpu = 0.014 (sec), leaf count = 24

$$\{\frac{x^4}{4}+3x^{2}y\left(x\right)+3x{\left(y\left(x\right)\right)}^2+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[x^3 + 3*y[x]*(2*x + y[x]) + 3*x*(x + 2*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(3*x^2 + Sqrt[9*x^4 - 3*x^5 + 36*x*C[1]])/(6*x)}, {y[x] -> (-3*x^2 + 
Sqrt[9*x^4 - 3*x^5 + 36*x*C[1]])/(6*x)}}

Maple raw input

dsolve(3*x*(x+2*y(x))*diff(y(x),x)+x^3+3*y(x)*(2*x+y(x)) = 0, y(x),'implicit')

Maple raw output

1/4*x^4+3*x^2*y(x)+3*x*y(x)^2+_C1 = 0