5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: 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. d. Compute the time t when N is changing the fastest using the initial condition N(0) = 2. Compare your answer to your qualitative estimate in part a(iii) above. e. Use Euler's Method with step sizes of h = 1 and then h = 0.1 to approximate the solution to the differential equation for N(0.5) and N(5). Find the relative error at %3D

5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: 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. d. Compute the time t when N is changing the fastest using the initial condition N(0) = 2. Compare your answer to your qualitative estimate in part a(iii) above. e. Use Euler's Method with step sizes of h = 1 and then h = 0.1 to approximate the solution to the differential equation for N(0.5) and N(5). Find the relative error at %3D

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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:
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.
hloi
d. Compute the time t when N is changing the fastest using the initial condition N(0) =
2. Compare your answer to your qualitative estimate in part a(iii) above.
%3D
= 0.1 to approximate the
solution to the differential equation for N(0.5) and N(5). Find the relative error at
moo mo these values. Obtain graphical plots of the numerical solution. How do they compare
se. Use Euler's Method with step sizes of h = 1 and then h
%3D
er to the plots of the actual solution?

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Please help for c and d.
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