4.14.25 \(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\)

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

\[ \left \{ \ln \relax (x ) +{\frac { \left (y \relax (x ) \right ) ^{2}}{6}}+{\frac {\ln \left (y \relax (x ) \right ) }{3}}+{\it \_C1}=0 \right \} \] 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