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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ANSWER To find the full solution and the steady solution for the given partial differential equation PDE and boundary conditions we can use the method of separation of variables The given PDE is ut co... View the full answer