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I have differential equation.

$y'=-ay^2$ where $a$ is a constant. My question is: is this logistic equation?

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    I am talking in the sense that $y(t)= \frac{M}{1+ce^{-aMt}}$ where $c$ is a constant.2012-11-14

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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 $y'=y-y^2.$

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    I couldn't agree more. It's like calling $y'' = \frac{1}{y^2}$ the _degenerate gravitational equation_.2012-11-14
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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.