Problem 2 (40 points) A cylindrical pipe with inner radius 1cm and wall thickness of 2.5cm carries a fluid at a temperature of 600C. The outer wall of the pipe is at 25C. The governing equation for the temperature distribution in the pipe wall is: r(dr2d2T)+drdT=500 Subject to the boundary conditions: T(1)=600C and T(3.5)=25C. It is desired to find the temperature distribution from r=1 to r=3.5cm at five equally spaced subintervals. a) Discretize the ODE using central difference formula for the derivatives for each subinterval. Use two-point and three point for the first and second order derivatives respectively. b) Express the system of equations obtained in part a in the form of Ax=b. c) Find the temperature distribution using LU decomposition