Following Problem -

7. [# 2.3.8.h) Solve the linear homogeneous InitialBoundary Value Problem: HEZkaIQu, U0, 1L(U,t) = 0, t > 0, u(L,t) = 0, t> 0, Mar, 0) = [(35), 0 0. Write each of the coefcients in terms of an integral of f(:i:). This corresponds to a oiledimensional rod either with heat loss through the lateral sides with outside temperature 0C or with insulated lateral sides with a heat sink proportional to the temperature. (Hint: Use separation of variables: Assume u(:i:, t) = (I)G(t). See first example in class but you will have a slightly different equation for one of the ODEs. Either cheek all possible As to find the eigenvalues or explain why the results from class still apply here.)