I need solving a problem in my diffential equations class. See attached images for details. Transcribed Image Text: According to Stefan’s law of radiation the

I need solving a problem in my diffential equations class. See attached images for details. Transcribed Image Text: According to Stefan’s law of radiation the absolute temperature Tof a body cooling in a medium at constant absolute temperature
Tm
is given by
dT
= k(T* – T),
‘m
dt
where k is a constant. Stefan’s law can be used over a greater temperature range than Newton’s law of cooling.
(a) Solve the differential equation.
(b) Show that when T- Tm is small in comparison to T then Newton’s law of cooling approximates Stefan’s law. [Hint: Think binomial series of the right-hand side of the DE.]
dT
= k(T* – T)
dt
= kTm
1 +
Using the binomial series, we expand the right side of the previous equation. (Enter the first three terms of the expansion.)
dT
= kT
dt
m
When T- Tm is small compared to
the third term in the expansion
vx can be ignored, giving
– z k¸(T – Tm), where k, = 4kT3.
dt

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