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By direct substitution into the heat equation and calculation of boundary values,

verify that the solution u(x, t) for a metal rod of length L which satisfies

the initial temperature u(x, 0) = f(x) and the boundary conditions

u(0, t) = u(L, t) = 0 is given by

u(x, t) = (sum)B(n)sin(npix/L)Dx

NB: Do not re-derive this formula, just verify that it satisfies the equation and

boundary conditions!]

i dont know how to do this without rederiving this equation,i do not know how to answer this question ,could anyone help

thanks