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,