4.707   y(x)(1 − 2x3y(x)2)+ x(1 − 2x2y (x)3)y′(x) = 0

ODE

y(x)(1 − 2x3y(x)2)+ x(1 − 2x2y(x)3)y′(x) = 0

ODE Classification

[_rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.031638 (sec), leaf count = 672

                                                                                                                                                                                                         (   )                                                                                                                                                                 (    )
(|(|           2  ------------------------x4(c1−-2x)2------------------------  3∘ -----8----27---3-6----√-∘--8-------4-----2-3----3-2-----5---------9-----4-    3)|  (|         2          ---------------------i-√3−ix4(c1−2x)2---------------------   (√ -   ) 3∘-----------------------------------------------------------
|||{|||{        c1x + ∘312c-x8−-6c2x7+c3x6+3√3∘x8-(−-24cx4+12c2x3−2c3x2+16x5+27)−-8x9−27x4 +  12c1x  − 6c1x  + c1x  + 3 3  x (− 24c1x + 12c1x − 2c1x + 16x + 27)− 8x − 27x − 2x |||}  |||{       2x (c1 − 2x�
   y(x) → ----------1----1---1-------------1----1----1-----------------------------------------------------------------------------------------------------  , y(x) → -----------------1----1---1-------------1-----1----1-------------------------------------------------------------------------------------------------------- ,  y(x) → -----------------1----1---1-------------1----1----1---------------
||||||                                                                               6x2                                                                       |||  |||                                                                                   12x2                                                                           |||  |||                                                                                   12x2                                                                            |
|(|(                                                                                                                                                         |)  |(                                                                                                                                                                  |)  |(                                                                                                                                                                   |

Maple
cpu = 0.119 (sec), leaf count = 21

{                                }
  − 2x −----1---2-− 2y(x)+ -C1 = 0
        2x2(y(x))

Mathematica raw input

DSolve[y[x]*(1 - 2*x^3*y[x]^2) + x*(1 - 2*x^2*y[x]^3)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-2*x^3 + x^2*C[1] + (x^4*(-2*x + C[1])^2)/(-27*x^4 - 8*x^9 + 12*x^8*C
[1] - 6*x^7*C[1]^2 + x^6*C[1]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] 
+ 12*x^3*C[1]^2 - 2*x^2*C[1]^3)])^(1/3) + (-27*x^4 - 8*x^9 + 12*x^8*C[1] - 6*x^7
*C[1]^2 + x^6*C[1]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] + 12*x^3*C[
1]^2 - 2*x^2*C[1]^3)])^(1/3))/(6*x^2)}, {y[x] -> (2*x^2*(-2*x + C[1]) - (I*(-I +
 Sqrt[3])*x^4*(-2*x + C[1])^2)/(-27*x^4 - 8*x^9 + 12*x^8*C[1] - 6*x^7*C[1]^2 + x
^6*C[1]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] + 12*x^3*C[1]^2 - 2*x^
2*C[1]^3)])^(1/3) + I*(I + Sqrt[3])*(-27*x^4 - 8*x^9 + 12*x^8*C[1] - 6*x^7*C[1]^
2 + x^6*C[1]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] + 12*x^3*C[1]^2 -
 2*x^2*C[1]^3)])^(1/3))/(12*x^2)}, {y[x] -> (2*x^2*(-2*x + C[1]) + (I*(I + Sqrt[
3])*x^4*(-2*x + C[1])^2)/(-27*x^4 - 8*x^9 + 12*x^8*C[1] - 6*x^7*C[1]^2 + x^6*C[1
]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] + 12*x^3*C[1]^2 - 2*x^2*C[1]
^3)])^(1/3) - (1 + I*Sqrt[3])*(-27*x^4 - 8*x^9 + 12*x^8*C[1] - 6*x^7*C[1]^2 + x^
6*C[1]^3 + 3*Sqrt[3]*Sqrt[x^8*(27 + 16*x^5 - 24*x^4*C[1] + 12*x^3*C[1]^2 - 2*x^2
*C[1]^3)])^(1/3))/(12*x^2)}}

Maple raw input

dsolve(x*(1-2*x^2*y(x)^3)*diff(y(x),x)+(1-2*x^3*y(x)^2)*y(x) = 0, y(x),'implicit')

Maple raw output

-2*x-1/2/y(x)^2/x^2-2*y(x)+_C1 = 0