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Show that (4) is a solution of $\frac{d p}{d t}=k p(1-p).$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Missouri State University

Campbell University

Harvey Mudd College

Lectures

02:12

Find particular solutions.…

02:07

Solve.$$\frac{d P}{d t…

00:47

Solve the equations.$$…

00:39

Solve the equation. Check …

00:48

Solve the equation using t…

01:40

Solve equation, and check …

01:41

Solve the equation by usin…

00:31

Solve each equation and ch…

Okay, So what we have here is a differential equation for you were asked to find solutions. Given an initial condition that easy go to zero basic one. So we were going to look at our example. We know that this differential equations a separable equation so we can rearrange it and write us the baby over B plus for is equality people. So integrating both sides of our vision will have and then o b plus four. It's equal to be let's see. So we want the further simplify this equation and we do this by getting the power of the both sides So we'll write e raise the Ellen off people spore. Is it what the series being, Let's see? So we know that the left side will just be equal to be dressed for and no, we seize this a consent and you can take any value. We can write the right side seeing erase with Pete said these So we can further simplify this and we'll have Bean is equal to see earrings that be minus four. So this is all war general solution. So we want to find its particular solution and we make use of the initial conditions given a while ago, which is a physical. 20 Be easy. Local 100. So he sucks. It'd be so over genital solution and we'll get 100 is equal to see erased zero minus sport. So this will just be equal. The one and we'll get C is equal to 100 port rewriting the whole equation. We now have the off P is equal to 104 series to be minus fort. So this is our particular. So you show

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