Dear all,
I'm having some trouble with the following question involving modelling with a first-order differential equation. My solution is below but it differs from the given answer. I also can't see where I might have erred.
Thank you.
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18. Consider an insulated box (a building, perhaps) with internal temperature
. According to Newton's law of cooling,
satisfies the differential equation
,
where
is the external temperature. Suppose that
varies sinusoidally; assume that
a) Solve the differential equation above and express
in terms of
.
My solution:
The above ODE is a linear equation. Rearrangement gives:
.
This linear ODE has integrating factor
.
Therefore,