Ut = Uxx e-3t sin(5x) + e−²t sin x, -2t u(0,t) = u(T,t) =0, u(x,0) = sin(2x).

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Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

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Q: What is the initial value of f(t) if its Laplace transform is 5-2? 2s(s+2)

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Q: Perform LU factorization for the following matrix. 1 1 1 1 L8 2 1 81 - 84

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