4.584   3x2y(x)y′(x)+ 2xy(x)2 + 1 = 0

ODE

3x2y(x)y′(x)+ 2xy(x)2 + 1 = 0

ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00776119 (sec), leaf count = 47

{ {          --------}  {         --------}}
           ∘  c1    2           ∘  c1   2
   y(x) → −   x4∕3-− x- , y(x) →   x4∕3 − x

Maple
cpu = 0.008 (sec), leaf count = 19

{(y(x))2 + 2x −1 −-C1x− 43 = 0}

Mathematica raw input

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

Mathematica raw output

{{y[x] -> -Sqrt[-2/x + C[1]/x^(4/3)]}, {y[x] -> Sqrt[-2/x + C[1]/x^(4/3)]}}

Maple raw input

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

Maple raw output

y(x)^2+2/x-1/x^(4/3)*_C1 = 0