Question: please solve on page complete Consider the heat equation Ut = C'urI + a COS(X - T) where c > 0 and a E R

please solve on page complete

Consider the heat equation Ut = C'urI + a COS(X - T) where c > 0 and a E R are given constants. a) Show that v(I, t) = cos(I - 7) is a solution of (1). b) Find the solution of equation (1) for x E [0, w] and t > 0 such that Us (0, t) = uz(7, t) = 0, t>0, and 0, u(x, 0) = 2cos(I - T) + - 7 , 2

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