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.
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 .
The above ODE is a linear equation. Rearrangement gives:
This linear ODE has integrating factor .
+ C, where C has absorbed the product of integration constants from both integrals with .
However, the given answer is: