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 = 4.63731 (sec), leaf count = 1

\[\text {$\$$Aborted}\]

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

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac {{b}^{2} \left (y \relax (x ) \right ) ^{4}+2\,ab \left (y \relax (x ) \right ) ^{3}x+{x}^{2} \left ({a}^{2}+{b}^{2}+1 \right ) \left (y \relax (x ) \right ) ^{2}+2\,aby \relax (x ) {x}^{3}+{a}^{2}{x}^{4}}{{x}^{4}}} \right ) }+\ln \left ({\frac {ax+by \relax (x ) }{x}} \right ) -\ln \relax (x ) -{\it \_C1}=0 \right \} \] 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),'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