4.2.33 \(y'(x)=x y(x)^3\)

ODE
\[ y'(x)=x y(x)^3 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

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

\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {-2 c_1-x^2}}\right \},\left \{y(x)\to \frac {1}{\sqrt {-2 c_1-x^2}}\right \}\right \}\]

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

\[ \left \{ \left (y \relax (x ) \right ) ^{-2}+{x}^{2}-{\it \_C1}=0 \right \} \] 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