3 (a) Use the method of separation of variables to find a solution u(x, t) of the fol- lowing homogeneous heat equation:

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3 A Use The Method Of Separation Of Variables To Find A Solution U X T Of The Fol Lowing Homogeneous Heat Equation 1 (30.3 KiB) Viewed 17 times

3 (a) Use the method of separation of variables to find a solution u(x, t) of the fol- lowing homogeneous heat equation: (z, t) - kurz(,t) = 0, 0 < x < L ,0 <t, u(0,t) = u(L, t) =0, 0 <t, u(3,0) = $(x), 0<x<L, where k > 0 is a given constant and is a given function. What assumption(s) should you make about the function o in order for this solution to be valid? (b) Write down a formula for the solution u(x, t) to the problem in part (a) when (x) is given by the following formula: p(x) = sin 10% -Cr). 2% 2% (c) Give a qualitative sketch of the graph of the solution u(x, t) that you found in part (b). 11..note the marimum