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Homework Statement
For many differential equations, the easiest way to find inflection points is to use the differential equation rather than the solution itself. To do this, we can compute [tex]y''[/tex] by differentiating [tex]y'[/tex], remembering to use the chain rule wherever [tex]y[/tex] occurs. Next, we can substitute for [tex]y'[/tex] by using the differential equation and setting [tex]y' = 0[/tex]. Then we can solve for [tex]y[/tex] to find the inflection points. (Keep in mind here that solving for [tex]y[/tex] can also produce some equilibrium solutions, which may not be inflection points!)
Use the technique described above to find the inflection point for the solutions of the differential equation
[tex]y'=r(1-\frac{y}{L})y[/tex]
your answer may contain [tex]L[/tex] and [tex]r[/tex]
[tex]y = ?[/tex]
The Attempt at a Solution
I differentiated the given equation and set it equal to zero, then I solved it for y. My answer was Lr/4 but this is wrong according to webworks.
The equation I got when I differentiated [tex]y'=r(1-\frac{y}{L})y[/tex] was [tex]y'' = r-((4y)/L)[/tex]
i know the answer is [tex]L/2[/tex] but I don't know how to get there.
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