Given: Pu The given boundary value problem is a² и (0, г) %3 dx2 0, t> 0, и (х, 0) —D f (x) and ди dt It=0 0, х Calculation: The given boundary value problem is, a² dx2 dt2 Take Fourier transform of both sides of the abo a²F { #u } = F{ #u} dx² dt2 d²U -a?a? U (a, t) + a² au (0, t) dt2 -a?a?U (a, t) = U (α, d²U dt2 Therefore, the equation is, d²U + a²a?U (a, t) = 0 dt2

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