For u(x,t) defined on the domain of 0 x 1 and t 0, find the full...
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For u(x,t) defined on the domain of 0 ≤x≤ 1 and t≥ 0, find the full solution for the PDE, J²u əx² ди at with the boundary conditions: (i) u(0, t) = 0, (ii) u(1,t) = 0, (iii) u(x,0) = sin(2x) + sin(3лx). In addition, also find the steady solution as t→∞o. For this problem, we expect a closed-form exact solution with only a finite number of terms and without any unevaluated integrals. This is required for both the full solution and the steady solution. Expect a deduction if the requirement is not satisfied. = cosh(t) +47² сosh(t) u, For u(x,t) defined on the domain of 0 ≤x≤ 1 and t≥ 0, find the full solution for the PDE, J²u əx² ди at with the boundary conditions: (i) u(0, t) = 0, (ii) u(1,t) = 0, (iii) u(x,0) = sin(2x) + sin(3лx). In addition, also find the steady solution as t→∞o. For this problem, we expect a closed-form exact solution with only a finite number of terms and without any unevaluated integrals. This is required for both the full solution and the steady solution. Expect a deduction if the requirement is not satisfied. = cosh(t) +47² сosh(t) u,
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