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