Solution of the Wave Equation by Separation of Variables
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چکیده
We are going to solve this problem in three steps. Step 1 In the first step, we find all solutions of (1) that are of the special form u(x, t) = X(x)T (t) for some function X(x) that depends on x but not t and some function T (t) that depends on t but not x. This is where the name “separation of variables” comes from. It is of course too much to expect that all solutions of (1) are of this form. But if we find a bunch of solutions Xi(x)Ti(t) of this form, then since (1) is a linear equation, ∑
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