Let A$($t$)=$ b$1$ cos$($t$)+$ b$2$ sin$($t$)$ be the ambient temperature in your kitchen,

which varies sinusoidally as function of time t$.$ Assume A$($t$)$ is known $$ that is$,$ the

values of b$1,$ b$2,$ and have been measured.

You have just cooked a cup of noodles. Newton$$s Law of Cooling states that the

temperature function y$($t$)$ of the noodles satisfies

y$=$k$($y $$ A$($t$))$

with k a $($known$)$ positive constant. The $$steady$-$state$$ solution $($which y

approaches in the limit as t increases$)$ is of the form

y$($t$)=$ c$1$ cos$($t$)+$ c$2$ sin$($t$).$

Use Newton$$s Law of Cooling to write b$1$ and b$2$ in terms of c$1,$ c$2.$ Write the linear

relations you found as a system of equations with kbi on the right side. Then use an

inverse matrix to find a formula for the steady$-$state solution.