Solve the heat conduction problem. ?"u/?x" = 1/2 ?u/?t , 0 < x < 3, t > 0 subject to the boundary conditions u(0, t) = u(3, t) = 0 and the initial condition. u(x, 0) = 5sin(4?x)
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First, we need to find the general solution to the heat conduction equation: a^2u_xx = u_t We assume a solution of the form u(x,t) = X(x)T(t), and substitute it into the equation: a^2X''T = XT' Dividing both sides by X(x)T(t), we get: (a^2/X(x)) X'' = Show more…
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