ди 10²u = It 40x²¹ together with the boundary conditions u(0, t) = 0 and u(, t) = 0 for t≥0 and the initial condition u(x, 0) = x(x) for 0 < x (a) If n is a positive integer, show that the function Un(x, t) = e-n²t sin(2nx), satisfies the given partial differential equation and boundary conditions. (b) The general solution of the partial differential equation that satisfies the boundary conditions is 8 u(x,t) = Σ Bhe e-n²t sin(2nx). n=1 Wnito d /1

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