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## Homework Statement

Suppose that [tex] y(t) [/tex] is a solution of the initial value problem

[tex] dy/dt = y(1-.0005y) , y(0) = 1 [/tex]

What is the limit [tex] \lim_{t\to\infty}y(t) [/tex]

## The Attempt at a Solution

If I try just separating it to solve for [tex]y(t)[/tex] then I get [tex]\int{{dy}/{(y-.0005y^2)}} = x+C[/tex] which I can't figure out how to solve. I'm at a loss as to what else to do. Is there some way I should be able to predict the behaviour of the function with just the initial value and the DE, or am I missing something about how to evaluate the integral or solve the DE? I tried predicting what the function would do based on what I was given, but I got the wrong answer and figured it was because I was doing it based on the y values, but not knowing the actual function I didn't know which y values would occur as t went to infinity.