4.12.8 $x(3y(x)+2x)y^{\prime }(x)+3(y(x)+x{)}^2=0$

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

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0279902 (sec), leaf count = 71

$$\{\{y(x)\to -\frac{\sqrt{6e^{4c_1}-2x^4}+4x^2}{6x}\},\{y(x)\to \frac{\sqrt{6e^{4c_1}-2x^4}-4x^2}{6x}\}\}$$

Maple ✓
cpu = 0.013 (sec), leaf count = 35

$$\{-\frac{1}{4}\ln \left(\frac{3x^2+8xy\left(x\right)+6{\left(y\left(x\right)\right)}^2}{x^2}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

-1/4*ln((3*x^2+8*x*y(x)+6*y(x)^2)/x^2)-ln(x)-_C1 = 0