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