What is the logistic equation that satisfies the initial condition of (0,4) where the logistic differential equation is #dy/dt=y(1-y/36)#?

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Answer 1 · 2018-01-21T10:26:52

#y=36/(1+8e^(-t))#

The general form of the differential equation is:

#dy/dt=k*y(1-y/L)#

in that form the solution is of the form:

#y=L/(1+Ae^(-kt))# where #A = (L-y_0)/y_0#.

(Arrived at through partial fraction decomposition and separation of variables. See this video for the solution. )

For this problem #k=1#, #L=36#, and #y_0=4#.

Calculating #A#:

#A=(36-4)/4=8#.

Substituting everything:

#y=36/(1+8e^(-t))#