Cubic logistic differential equation
= Cubic logistic differential equation
{title2=$2\dot y=y-y^3$}
The substitution $z=y^{-2}$ turns the nonzero solutions into $\dot z=1-z$. Thus $y=\pm(1+Ke^{-t})^{-1/2}$ where the denominator is positive, together with $y=0$. The nonzero <equilibrium points> $\pm1$ are attracting and $0$ is unstable. The sign of nonzero initial data is preserved.