Author Question: What is the second derivative of a logistic differential equation? (Read 1507 times)

Sandstorm

  • Sr. Member
  • ****
  • Posts: 268
I can manage integrating it, but how to I take the second derivative?

I have a partial formula written down, but it's incorrect.

Thanks!



coco

  • Hero Member
  • *****
  • Posts: 739
This is the original equation below:
X(t) = (1 + ( (1/x) -1)e^(-rt) ) ^-1

Solve the denominator :
X(t) = (1 + ( (1 - x)/x)e^(-rt) ) ^-1

Solve for the lowest denominator and bring to the numerator
X(t) = X(X + e^(-rt) - Xe^(-rt) ) ^-1

Now take the first derivative:
X'(t) = -X(-re^(-rt) + Xre^(-rt) ) ^-2

Then take the second derivative
X''(t) = 2X(r^2e^(-rt) - Xr^2e^(-rt) ) ^-3

Make the equation into a nice form:
X''(t) = 2X/(r^2e^(-rt) - Xr^2e^(-rt) )^3

You may go ahead to seperate common variables but the most important point is about the mastery of the concept.

I hope this helps.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
 

Did you know?

For high blood pressure (hypertension), a new class of drug, called a vasopeptidase blocker (inhibitor), has been developed. It decreases blood pressure by simultaneously dilating the peripheral arteries and increasing the body's loss of salt.

Did you know?

In Eastern Europe and Russia, interferon is administered intranasally in varied doses for the common cold and influenza. It is claimed that this treatment can lower the risk of infection by as much as 60–70%.

Did you know?

Nearly all drugs pass into human breast milk. How often a drug is taken influences the amount of drug that will pass into the milk. Medications taken 30 to 60 minutes before breastfeeding are likely to be at peak blood levels when the baby is nursing.

Did you know?

A recent study has found that following a diet rich in berries may slow down the aging process of the brain. This diet apparently helps to keep dopamine levels much higher than are seen in normal individuals who do not eat berries as a regular part of their diet as they enter their later years.

Did you know?

Bacteria have been found alive in a lake buried one half mile under ice in Antarctica.

For a complete list of videos, visit our video library