Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. c₁et 1+c₁et When P = dp dt dP dt dP dt Thus, in terms of t, ₁et 1+ C₁²(1. - = P(1-P); P = c₂e² 1+c₁et c₁et + Get) = 1400(1-1+r) Get Get

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
c₁et
1 + c₁et
When P =
dp
dt
=
dp
dt
dP
dt
= P(1-P); P =
Get
1+c₁et
Thus, in terms of t,
c₁et
₁0²(1.
1+ C₁6
Get
[
+ ₁₁et).
1 +
Get
+ Get (1-_G₁₂et
1+
1 +
Transcribed Image Text:Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. c₁et 1 + c₁et When P = dp dt = dp dt dP dt = P(1-P); P = Get 1+c₁et Thus, in terms of t, c₁et ₁0²(1. 1+ C₁6 Get [ + ₁₁et). 1 + Get + Get (1-_G₁₂et 1+ 1 +
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