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The function u(x, t) satisfies the partial differential equation
u/t=²u/x²; 0≤x≤3; t≥0
subject to the initial and boundary conditions
u(0,t) =0, u(3,t) = 0, u(x, 0) = x(1-x), (²u/x²)ₜ₌₀= sin πx
Find u(x,t).

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