ODE
\[ x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.342338 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )}\right \},\left \{y(x)\to \sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.098 (sec), leaf count = 14
\[\left [y \left (x \right ) = \frac {1}{\sqrt {\frac {1}{\LambertW \left (\frac {\textit {\_C1}}{x^{6}}\right )}}}\right ]\] Mathematica raw input
DSolve[3*x^2*y[x] + x^3*(1 + y[x]^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[ProductLog[E^(2*C[1])/x^6]]}, {y[x] -> Sqrt[ProductLog[E^(2*C[1])/x^6]]}}
Maple raw input
dsolve(x^3*(1+y(x)^2)*diff(y(x),x)+3*x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/(1/LambertW(_C1/x^6))^(1/2)]