(6) (Show manual calculations for this task) Let the partial differential equation J²u J²u U = Ət² əx² be given for 0 0 with associated marginal requirements u (0, t) = u(π, t) = 0 for t > 0 and start conditions u (x, 0) = 7 sin(4x) and u₁(x, 0) = 0 for 0 < x < . Determine u = u(x, t) by separation of variables.

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