In an experiment, a test tube containing a chemical is immersed in a water (c) bath. At r = 0, the temperature, H (t) of the chemical in the test tube is 27°C. The controlled temperature (measured in degrees Celcius) of the water bath is H, (t) = 38 –-22e",1> 0, where r is measured in minutes. Referring to the Newton's empirical law -k(H– H,), where k is the proportionality constant assumed to be 0.1 per minute, answer the following questions: %3D In words, discuss the profile of the temperature H (1) in the short term AND in the long term (Calculation is not needed). (1) (i) Solve this initial value problem.
In an experiment, a test tube containing a chemical is immersed in a water (c) bath. At r = 0, the temperature, H (t) of the chemical in the test tube is 27°C. The controlled temperature (measured in degrees Celcius) of the water bath is H, (t) = 38 –-22e",1> 0, where r is measured in minutes. Referring to the Newton's empirical law -k(H– H,), where k is the proportionality constant assumed to be 0.1 per minute, answer the following questions: %3D In words, discuss the profile of the temperature H (1) in the short term AND in the long term (Calculation is not needed). (1) (i) Solve this initial value problem.
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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For c
Transcribed Image Text:(a)
Given a differential equation r'x +2rx -tx +x= 122. Show that
x=÷+cx+c3tlnt +4r?
is a solution of the the differential equation. Assume an appropriate interval/
of definition.
Given a differential equation x =
(zx) that passes through a point (fo, xo).
(b)
determine a region of the rx-plane for which the differential equation would
have a unique solution.
(c)
In an experiment, a test tube containing a chemical is immersed in a water
bath. At = 0, the temperature, H (t) of the chemical in the test tube is 27°C.
The controlled temperature (measured in degrees Celcius) of the water bath
is H„ (1) = 38 –22e",1>0, where r is measured in minutes. Referring to the
Newton's empirical law -k(H-H,.), where k is the proportionality constant
assumed to be -0.1 per minute, answer the following questions:
In words, discuss the profile of the temperature H (1) in the shord term
AND in the long term (Calculation is not needed).
()
(i)
Solve this initial value problem.
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