Answer either Yes or No in the boxes provided. A population r of rats satisfies the DE da/ dt. kr2 Initially there are x(0) = 2 rats, and their number is increasing at the rate of dr/dt =1 rat per month when there are x = 10 rats. a) The value of the constant k is k=1/100? 100 x(t) = 50-t b) The solution of this initial value problem is lim x(t) = 0? c) t 50-

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Answer either Yes or No in the boxesprovided.
of rats satisfies the DE dx/ dt
kr2 Initially there are
x(0) = 2 rats, and
A population
their number is increasing at the rate of dr/dt =1 rat per month when there are
x = 10 rats.
a) The value of the constant is k = 1/100?
100 ?
x(t) = 50-t
b) The solution of this initial value problem is
lim x(t) = 0?
c)
t→50-
Transcribed Image Text:Answer either Yes or No in the boxesprovided. of rats satisfies the DE dx/ dt kr2 Initially there are x(0) = 2 rats, and A population their number is increasing at the rate of dr/dt =1 rat per month when there are x = 10 rats. a) The value of the constant is k = 1/100? 100 ? x(t) = 50-t b) The solution of this initial value problem is lim x(t) = 0? c) t→50-
Expert Solution
Step 1

The general solution of a differential equation always contains a constant of integration. The initial condition in an initial value problem is used to determine the integration constant.

A differential equation can be solved using the variable separation method. In this method, the terms with like variables are isolated on either side of the equation and then integrated with respect to the variables to yield the general solution.

steps

Step by step

Solved in 4 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,