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Unformatted text preview: ditions, to find the eigenvalues and eigenfunctions necessary to obtain the general series solution for v ( x , t ). Write down this solution. (d) (1 Point) If the initial condition for the ORIGINAL problem [i.e., for u ( x , t ) which satisfies PDE (1) and boundary conditions (2)], is given by u ( x , 0) = x , find the initial condition for v ( x , t ). (e) (1 Point) Explain how you would use this initial condition for v ( x , t ) to find all the constants in the corresponding series solution of v ( x , t ). For an extra point, find all the constants and write down the complete solution for u ( x , t ); note that sin sin = 1 2 [ cos ( + )-cos(-)]....
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- Spring '07