Q4. (a) The temperature u(x, t) in a rod of length - is determined from the following boundary value problem. uz = Uxx, 0 < x 0 u(0,t) = 0,t > 0 u (5.t) = 0, t > 0 u(x,0) = 5sin(6x), 0 < x < 2 Use the method of separation of variables to find the temperature u(x,t). (b) Find the half-range sine series expansion of the function f(x) = 3,0 < x < n.

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