4.714   y(x)y′(x)((ax + by(x))3 + ax3)+ x((ax +by(x))3 + by(x)3) = 0

ODE

y(x)y′(x )((ax + by(x))3 + ax3)+ 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

$Aborted

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

{     (         4          3      (         )      2                 )     (          )                }
 − 1 ln  b2(y(x))-+-2ab(y(x))-x-+-x2-a2 +-b2 +-1-(y(x))-+-2aby(x)x3 +-a2x4 + ln ax-+-by(x) − ln(x)− -C1 = 0
   2                                  x4                                        x

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