The boundary value problem for a heated rod with insulated ends has the formal series solution: u(x,t) =+ 2 a,exp(-n²n?kt/L²) cos- n=D1 where the {an} are the Fourier cosine series coefficients in an = S(x)cosdx for n = 0,1,2,. %3D of the rod's initial temperature function f(x) = u(x,0). %3D Use the formula above for the following boundary value problem 2u, = urx, 0

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