chapter 9 Differential Equations (9.5 Linear Equations (Application to…
chapter 9 Differential Equations
9.5 Linear Equations
Application to Electric Circuits
9.4 Models for Population
The Logistic Model
Multiplying by P, we obtain the model for population growth
known as the logistic differential equation:
The Law of Natural Growth
negative, it decreases.
If k is positive, then the population increases; if k is
Equation 1 is sometimes called the law of natural growth.
9.1 Modeling with Differential
Show that every member of the family of functions
is a solution of the differential equation .
9.2 Direction Fields and Euler's Method
9.3 Separable Equations
Find the orthogonal trajectories of the family of curves x = ky2, where is k an arbitrary constant.
The curves x = ky2 form a family of parabolas whose axis of symmetry is the x-axis.
The first step is to find a single differential equation that is satisfied by all members of the family.
If we differentiate x = ky2, we get