##### 4.15.14 $$y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0$$

ODE
$y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0$ ODE Classiﬁcation

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

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 4.2526 (sec), leaf count = 1

$\text {\Aborted}$

Maple
cpu = 0.606 (sec), leaf count = 160

$\left [y \left (x \right ) = \frac {x \left (x \textit {\_C1} -a \RootOf \left (a^{2} \textit {\_Z}^{4}-2 a x \textit {\_C1} \,\textit {\_Z}^{3}+\left (a^{2} x^{2} \textit {\_C1}^{2}+b^{2} x^{2} \textit {\_C1}^{2}+\textit {\_C1}^{2} x^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} \textit {\_C1}^{3} \textit {\_Z} +x^{4} \textit {\_C1}^{4}\right )\right )}{b \RootOf \left (a^{2} \textit {\_Z}^{4}-2 a x \textit {\_C1} \,\textit {\_Z}^{3}+\left (a^{2} x^{2} \textit {\_C1}^{2}+b^{2} x^{2} \textit {\_C1}^{2}+\textit {\_C1}^{2} x^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} \textit {\_C1}^{3} \textit {\_Z} +x^{4} \textit {\_C1}^{4}\right )}\right ]$ 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))

Maple raw output

[y(x) = x*(x*_C1-a*RootOf(a^2*_Z^4-2*a*x*_C1*_Z^3+(_C1^2*a^2*x^2+_C1^2*b^2*x^2+_
C1^2*x^2-b^2)*_Z^2-2*a*x^3*_C1^3*_Z+x^4*_C1^4))/b/RootOf(a^2*_Z^4-2*a*x*_C1*_Z^3
+(_C1^2*a^2*x^2+_C1^2*b^2*x^2+_C1^2*x^2-b^2)*_Z^2-2*a*x^3*_C1^3*_Z+x^4*_C1^4)]