Problem 8E

Problem

In Problems 1–12, a differential equation is given along with the field or problem area in which it arises. Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

= kp (P - P), where k and P are constants

(logistic curve, epidemiology, economics)

Solution :

Step 1 :

In this problem we have to explain the properties of logistic curve, epidemiology, economics.

Given equation is

where k and p are constant.

This equation contain only one derivative so it as ordinary differential equation.

And also it contain only one derivative( so it as first order.

In this equation independent variable is t,

And dependent variable is p.

This is nonlinear equation.

Hence this equation is nonlinear first order ordinary differential equation.