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• 22:47, 17 April 2024 Rice talk contribs created page Logistic equation (Created page with "Of the form <math>\begin{cases} y' = y(1 - y)\\ y(0)=y_0 \end{cases}</math> The solution is <math>y(t) = \frac{y_0e^t}{y_0 e^t - (y_0 - 1)}</math> = Analysis = ''y'' is undefined at <math>t = \ln \left( \frac{y_0 - 1}{y_0} \right)</math> If ''0 < y_0 < 1,'' The solution is defined for all ''t.'' ''y(t)'' approaches 1 as t approaches infinity. ''y(t)'' approaches 0 as ''t'' approaches negative infinity. For ''y_0 > 1,'' the blowup time is negative <math>\ln \left(...") Tag: Visual edit