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 = 0.0110813 (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 = 0.007 (sec), leaf count = 18
\[ \left \{ \ln \left ( x \right ) +{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{6}}+{\frac {\ln \left ( y \left ( x \right ) \right ) }{3}}+{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
ln(x)+1/6*y(x)^2+1/3*ln(y(x))+_C1 = 0