4.695   x (x− y(x)3)y′(x) = y(x)(y(x)3 + 3x)

ODE

x (x− y(x)3) y′(x) = y(x)(y(x)3 + 3x)

ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.127114 (sec), leaf count = 359

(                                          -------------------------                                                                      (        (      )(                  )                   ) )
|{({                     8c1               3∘ √-∘ ---6--8c1-----8-    7)}  ({        i√ 63 (√3-+ i)(√3-∘−-x6(e8c1-− 27x8)− 9x7) 2∕3 − (√3-+ 3i)e8c13 x2 )} |{     −1−i√3  √3∘
   y(x) → ∘-----------e-3--------------+ ---3--−-x-(e--−-27x-)−-9x-- ,  y(x) → ------------------∘--------------------------------------  , y(x) → -------------∘x2--------------+-i--3--3-+-i-e3--
|((        3 3√3∘ −-x6(e8c1 −-27x8)− 27x7            32∕3x2          )  (                   2 35∕6x2 3√3-∘ − x6-(e8c1 −-27x8)− 9x7          ) |(                2 32∕3 3 √3∘ −-x6(e8c1 −-27x8)− 9x7     |

Maple
cpu = 0.021 (sec), leaf count = 33

{                 (      3    )       (       )    }
  ln (x) − C1 + 3 ln  (y(x))-+-2x  − 3 ln  y(x)-1√-- = 0
              8         x         8         3x

Mathematica raw input

DSolve[x*(x - y[x]^3)*y'[x] == y[x]*(3*x + y[x]^3),y[x],x]

Mathematica raw output

{{y[x] -> (-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1/3)/(3^(2/3)*x
^2) + E^((8*C[1])/3)/(-27*x^7 + 3*Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1
/3)}, {y[x] -> (-((3*I + Sqrt[3])*E^((8*C[1])/3)*x^2) + I*3^(1/6)*(I + Sqrt[3])*
(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(2/3))/(2*3^(5/6)*x^2*(-9*
x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*C[1]) - 27*x^8))])^(1/3))}, {y[x] -> (I*3^(1/3)*(
I + Sqrt[3])*E^((8*C[1])/3) + ((-1 - I*Sqrt[3])*(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^
(8*C[1]) - 27*x^8))])^(2/3))/x^2)/(2*3^(2/3)*(-9*x^7 + Sqrt[3]*Sqrt[-(x^6*(E^(8*
C[1]) - 27*x^8))])^(1/3))}}

Maple raw input

dsolve(x*(x-y(x)^3)*diff(y(x),x) = (3*x+y(x)^3)*y(x), y(x),'implicit')

Maple raw output

ln(x)-_C1+3/8*ln((y(x)^3+2*x)/x)-3/8*ln(1/x^(1/3)*y(x)) = 0