Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...

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Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0 <x < 6; t > 0; B. C. : u, (0, t) = 0; Uz(6, t) = 0; t> 0; I. C. : u(x, 0) = 12 + 5cos (x) – 4cos(2nx); 0 <x < 6 (a) When t 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed Dirichlet-Neumann. Then, state the general solution for u(x, t). (Note: you don't need to derive the general solution u(x, t).) (7 marks) (c) Find the particular solution of this initial-boundary value problem making use of your general solution in Q2(b). (10 marks) Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0 <x < 6; t > 0; B. C. : u, (0, t) = 0; Uz(6, t) = 0; t> 0; I. C. : u(x, 0) = 12 + 5cos (x) – 4cos(2nx); 0 <x < 6 (a) When t 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed Dirichlet-Neumann. Then, state the general solution for u(x, t). (Note: you don't need to derive the general solution u(x, t).) (7 marks) (c) Find the particular solution of this initial-boundary value problem making use of your general solution in Q2(b). (10 marks)