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The temperature , u(x,t), in a metal rod of length L satisfies           del u/ del t =...

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Basic Math

The temperature , u(x,t), in a metal rod of length Lsatisfies
          del u/ del t= k del squared u / del x squared limit 0 less than or equal to, xless than or equal to L , t greater than or equal to 0

The ends of the rod at x=0 and x=L , are maintained ata constant temperature T not 0 , so that the boundary conditionsare
               u(0, t) =0    u(L, t) = 0
The initial temperature distribution is
      u(x,0) = 4 sin 2 pi x/ L - 6sin (3pi x/L) +12 sin (5 pi x / L)
Find the temperature, u(x, t).

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