Please determine the specific solution to the following nonh

Please determine the specific solution to the following non-homogenous PDE

Thank you!

Please solve in u(x,t) = To(t) + Sum[Tn(t)*Cos[n*Pi*x/L] form if possible

a(z, 0) =-10 cos(r) + 200s(2x) + 10 cos( 2 cos(2z) (22) cos(6e), cos(61),

Solution

Sherry is a wine that is typically aged in a series of barrels called a solera. Each year, a portion (assume half) of the wine in the last barrel is extracted, bottled, and sold. This barrel is then refilled with wine from the next-to-last barrel. The next-to-last barrel is then refilled with wine from the previous barrel, and the process is repeated until the first barrel is refilled with newly crushed juice from this year’s grape harvest. a. To understand the way that the solera system mixes and ages the wine, consider a thought experiment in which x[n] units of a tracer substance (such as deuterium) are added to the new crushed juice in year n. Let a[n], b[n], and c[n] represent the amount of tracer found in the first, second, and third barrels at the end of year n (i.e., after the wine to sell in year n has been drawn out and the crushed joice from year n has been added). Develop difference equations to determine a[n], b[n], and c[n] for n 0. b. Assume that one unit of tracer is added in year 0 and no tracer is added in any other year. Determine the year (or years) during which the amount of tracer in the third barrel is greatest. [Feel free to use a pencil, calculator, or computer to answer this question.] c. Assume that one unit of tracer is added each year. Determine the steady-state value of tracer in the first barrel, i.e., determine ass = limn a[n] [again, pencils, calculators, or computers are welcome]