chapter 9 Differential Equations (9.5 Linear Equations (Application to…
chapter 9 Differential Equations
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
9.4 Models for Population
The Law of Natural Growth
Equation 1 is sometimes called the law of natural growth.
If k is positive, then the population increases; if k is
negative, it decreases.
The Logistic Model
Multiplying by P, we obtain the model for population growth
known as the logistic differential equation:
9.5 Linear Equations
Application to Electric Circuits