Your assignment, solve Newton's Law of Colling/Heating Diffy Q below: dT - = k(M – T) dt To show that the solution to this differential equation produce the following: a) T(t)= M +(T,– M)e* k>0, T,>M b) т()- м- (м-т,)е " k>0, т, «м – kt With equation a) is for cooling, and Equation b) is for heating. Tis the temperature of the object at a given time t, M is the temperature of the surrounding medium, and k is a positive constant. To is the initial temperature of the object- the condition given to find particular solution to the differential equation!

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Your assignment, solve Newton's Law of Colling/Heating Diffy Q below:
dT
= k(M -T)
dt
To show that the solution to this differential equation produce the following:
а) т()- м+(т -м)е* k>0, Т, > м
- kt
b) т() - м-(м-т,)е " k>0, Т, <м
-kt
= M-
With equation a) is for cooling, and Equation b) is for heating.
Tis the temperature of the object at a given time t, M is the temperature of the surrounding medium,
and k is a positive constant. To is the initial temperature of the object- the condition given to find
particular solution to the differential equation!
Transcribed Image Text:Your assignment, solve Newton's Law of Colling/Heating Diffy Q below: dT = k(M -T) dt To show that the solution to this differential equation produce the following: а) т()- м+(т -м)е* k>0, Т, > м - kt b) т() - м-(м-т,)е " k>0, Т, <м -kt = M- With equation a) is for cooling, and Equation b) is for heating. Tis the temperature of the object at a given time t, M is the temperature of the surrounding medium, and k is a positive constant. To is the initial temperature of the object- the condition given to find particular solution to the differential equation!
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