4.15.14 $y(x)y^{\prime }(x)((ax+by(x){)}^3+a{x}^3)+x((ax+by(x){)}^3+by(x{)}^3)=0$

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

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

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 4.63731 (sec), leaf count = 1

$$\mathrm{\$}\text{Aborted}$$

Maple ✓
cpu = 0.045 (sec), leaf count = 81

$$\{-\frac{1}{2}\ln \left(\frac{b^2{\left(y\left(x\right)\right)}^4+2ab{\left(y\left(x\right)\right)}^{3}x+x^2(a^2+b^2+1){\left(y\left(x\right)\right)}^2+2aby\left(x\right)x^3+a^2{x}^4}{x^4}\right)+\ln \left(\frac{ax+by\left(x\right)}{x}\right)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

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