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, (b) ди ди = 9 at მე2 0 < x <5, t >0 du du The boundary conditions are, 0 (0, t) = 0 (5,t) = 0, for t≥0, дх дх and the initial condition is, u(x, 0) = {0, 0<x<2 (i) (11) (111) x 2<x<5 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 arrive at the general solution.) (5 marks) Solve for a solution for u(x, t). (Assuming that it is an even function) (8 marks) 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)