dN %3D dt = 0.25N(10 - N), N(0) = 2 (a) %3D where N is measured in 100's. Analyze the behavior of this differential equation as follows. b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field plot. Compare it to your qualitative plot in part (a) above. c. Solve this differential equation using the separation of variables technique. Plot the solution over the interval of time from [0, 10]. How does your actual solution compare to the qualitative graphical solution?
dN %3D dt = 0.25N(10 - N), N(0) = 2 (a) %3D where N is measured in 100's. Analyze the behavior of this differential equation as follows. b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field plot. Compare it to your qualitative plot in part (a) above. c. Solve this differential equation using the separation of variables technique. Plot the solution over the interval of time from [0, 10]. How does your actual solution compare to the qualitative graphical solution?
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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![5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
w
dN
= 0.25N(10 – N), N(0) = 2
dt
(a)
|
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field
plot. Compare it to your qualitative plot in part (a) above.
c. Solve this differential equation using the separation of variables technique. Plot the
solution over the interval of time from [0, 10]. How does your actual solution compare
to the qualitative graphical solution?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64c780d2-a8a0-4ff8-a74c-59396aa6e397%2F9f7889a5-8726-4fbf-89d5-c1acc26fecc7%2F565tdd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
w
dN
= 0.25N(10 – N), N(0) = 2
dt
(a)
|
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
b. Obtain a slope field plot of this differential equation. Briefly analyze the slope field
plot. Compare it to your qualitative plot in part (a) above.
c. Solve this differential equation using the separation of variables technique. Plot the
solution over the interval of time from [0, 10]. How does your actual solution compare
to the qualitative graphical solution?
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