7- Bernoulli equations

(lecture 8 on slides) lots o f solving stuff that couldnt be put on the flashacrds

What is the Bernoulli equation?

A Bernoulli equation is a first-order nonlinear ODE of the form:

When is the Bernoulli equation already linear?

How do we transform a Bernoulli equation into a linear ODE?

What is the transformed bernoullli equation after substitution?

What are the steps to solve the Bernoulli equation?

What is the simplest model for population growth?

What is the logistic equation for population growth?

• k>0 is the growth rate,

• A is the carrying capacity, representing the maximum sustainable population.

What are the three possible solutions of the logistic equation?

What is the general form of the logistic function?

• L is the maximum value of the function

• k is the logistic growth rate,

• x₀ is the x-value of the midpoint of the curve.