I have differential equation.
$y'=-ay^2$ where $a$ is a constant. My question is: is this logistic equation?
I have differential equation.
$y'=-ay^2$ where $a$ is a constant. My question is: is this logistic equation?
If so, it's a degenerate one. But to my mind, only equations of the form $y'=ay-by^2$ with $a,b>0$ qualify as logistic. In a sense there is only one logistic equation, as a suitable rescaling always renders a logistic equation in its standard form $y'=y-y^2.$
One can determine that the solutions to this equation are $y=0$ and those of the form $y=\cfrac1{at+C}$ for some constant $C$. These aren't logistic.