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A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their number is increasing at the rate of dx/dt = 1 rat per month when there are x = 10 rats.

A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their number is increasing at the rate of dx/dt = 1 rat per month when there are x = 10 rats.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A population of rats satisfies the DE dx /dt ka?. = Initially there are x(0) = 2 rats, and their number is increasing at the rate of dx/dt = 1 rat per month when there are r x = 10 rats.
Transcribed Image Text:A population of rats satisfies the DE dx /dt ka?. = Initially there are x(0) = 2 rats, and their number is increasing at the rate of dx/dt = 1 rat per month when there are r x = 10 rats.
a) The value of the constant k is k = 1/100? b) The solution of this is r(t) = initial value problem 100 ? 50-t lim x(t) = 0? c) t→50-
Transcribed Image Text:a) The value of the constant k is k = 1/100? b) The solution of this is r(t) = initial value problem 100 ? 50-t lim x(t) = 0? c) t→50-
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