4.2.33 $y^{\prime }(x)=xy(x{)}^3$

ODE
$$y^{\prime }(x)=xy(x{)}^3$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.00579969 (sec), leaf count = 39

$$\{\{y(x)\to -\frac{1}{\sqrt{-2c_1-x^2}}\},\{y(x)\to \frac{1}{\sqrt{-2c_1-x^2}}\}\}$$

Maple ✓
cpu = 0.005 (sec), leaf count = 14

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

DSolve[y'[x] == x*y[x]^3,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

1/y(x)^2+x^2-_C1 = 0