Q4(a) A cable of length 5 cm has its ends insulated and the initial temperature distribution...

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Q4(a) A cable of length 5 cm has its ends insulated and the initial temperature distribution is given by u(x, 0) = f(x)°C. The heat equation and the conditions are as follow, ди a'u 0 < x < 5, t >0 %3D at du du The boundary conditions are, " (0, t) = (5, t) = 0, fort2 0, (0, 0<x< 2 x 2sx<5 and the initial condition is, u(x, 0) = (1) Explain whether this is a case of Dirichlet, Neumann, or mixed Dirichlet-Neumann problem. (2 marks) Based on your answer from Q4(a), identify the general solution for the temperature distribution u(x, t). (Note: you are not required to show the steps on how you arive at the general solution.) (5 marks) (iii) Solve for a solution for u(x, t). (Assuming that it is an even function) (8 marks) (b) Consider the differential equation and the initial condition below: y" + 2xy' = 0, y(0) = 3, y'(0) = 0 Find the recurrence relation for the coefficients of the power series solution. (5 marks) Q4(a) A cable of length 5 cm has its ends insulated and the initial temperature distribution is given by u(x, 0) = f(x)°C. The heat equation and the conditions are as follow, ди a'u 0 < x < 5, t >0 %3D at du du The boundary conditions are, " (0, t) = (5, t) = 0, fort2 0, (0, 0<x< 2 x 2sx<5 and the initial condition is, u(x, 0) = (1) Explain whether this is a case of Dirichlet, Neumann, or mixed Dirichlet-Neumann problem. (2 marks) Based on your answer from Q4(a), identify the general solution for the temperature distribution u(x, t). (Note: you are not required to show the steps on how you arive at the general solution.) (5 marks) (iii) Solve for a solution for u(x, t). (Assuming that it is an even function) (8 marks) (b) Consider the differential equation and the initial condition below: y" + 2xy' = 0, y(0) = 3, y'(0) = 0 Find the recurrence relation for the coefficients of the power series solution. (5 marks)