\begin{aligned} &\text { (a) Show that the solution to } y^{\prime}+p y=g(t), \text { where } p \text { is a constant can be written as }\\ &y(t)=y_{0} e^{-p t}+e^{-p

t} * g(t) \end{aligned} Here, we have n tanks, each with constant volume V of pure water. At time t = 0,a solution with concentration c grams of salt per litre flows into Tank 1 at a rate of r litres per minute, and the well-stirred mixture flows out of Tank 1 and into Tank 2 at the same rate, and so on. Calculate the quantity Q„(t), the mass of salt at time t in Tank n. Express your answer as an integral, but do NOT evaluate it.Hint: use previous question(s) and the convolution theorem. (c) Aside from using a computer, how would you solve the integral in part (b) for a given value of n? Do not evaluate the integral, but rather explain in a sentence or two, including the name of the method used.

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