4.6.24 $x^2{y}^{\prime }(x)=2y(x)(x-y(x{)}^2)$

ODE
$$x^2{y}^{\prime }(x)=2y(x)(x-y(x{)}^2)$$ ODE Classification

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

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.00889937 (sec), leaf count = 46

$$\{\{y(x)\to -\frac{x^2}{\sqrt{c_1+\frac{4x^3}{3}}}\},\{y(x)\to \frac{x^2}{\sqrt{c_1+\frac{4x^3}{3}}}\}\}$$

Maple ✓
cpu = 0.006 (sec), leaf count = 19

$$\{{\left(y\left(x\right)\right)}^{-2}-\frac{4}{3x}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^4}=0\}$$ Mathematica raw input

DSolve[x^2*y'[x] == 2*y[x]*(x - y[x]^2),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^2*diff(y(x),x) = 2*y(x)*(x-y(x)^2), y(x),'implicit')

Maple raw output

1/y(x)^2-4/3/x-1/x^4*_C1 = 0