ODE
\[ y'(x)=x y(x)^3 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.216002 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {-x^2-2 c_1}}\right \},\left \{y(x)\to \frac {1}{\sqrt {-x^2-2 c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {1}{\sqrt {-x^{2}+\textit {\_C1}}}, y \left (x \right ) = -\frac {1}{\sqrt {-x^{2}+\textit {\_C1}}}\right ]\] 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))
Maple raw output
[y(x) = 1/(-x^2+_C1)^(1/2), y(x) = -1/(-x^2+_C1)^(1/2)]