Verifying Heat Equation in Metal Rod: Help Needed!

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SUMMARY

The discussion focuses on verifying the solution of the heat equation for a metal rod of length L, specifically the solution u(x, t) = (sum)B(n)sin(npix/L)Dx. Participants emphasize the importance of direct substitution into the heat equation and calculating boundary values to confirm that the initial temperature u(x, 0) = f(x) and boundary conditions u(0, t) = u(L, t) = 0 are satisfied. The main challenge highlighted is the need to demonstrate that the left-hand side (LHS) equals the right-hand side (RHS) without re-deriving the formula.

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can anyone help me interpret what exactly this question is asking as i am quite unawares

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 don't know how to do this without rederiving this equation,i do not know how to answer this question ,could anyone help
thanks
 
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ie. put your given solution into the equation and show that LHS =RHS
 

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