Solve the following heat equation ?u/?t = ?²u/?x² with the boundary conditions u(0, t) = 0 u(2, t) = 0 and the initial condition u(x, 0) = 3sin(2?x)
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We assume that the solution can be written as a product of two functions, one depending only on x and the other only on t. So, we write u(x,t) = X(x)T(t). Substituting this into the heat equation, we get X''(x)T(t) = X(x)T'(t). Dividing both sides by X(x)T(t), we Show more…
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