Solution to Bessel and Legendre Equations 1.) Write the two linearly independent solutions of the equations below and show the process involved in arriving at these solutions. d?u 1 du а.) + + u = 0...

Extracted text: Solution to Bessel and Legendre Equations 1.) Write the two linearly independent solutions of the equations below and show the process involved in arriving at these solutions. d?u 1 du а.) + + u = 0 dz2 z dz d?u du b.) ++ 4xu = 0 dx %3D dx2 d²y 2х dy 3 + х2-1 dx y = 0 с.) dx2 х2-1 2.) Using Matlab, separately plot the solutions mentioned above. Assume arbitrary constants involved in each solution equal to unity. Submit result of sample run and write a short discussion for each graph. In producing the result of sample run, use Publish feature of Matlab and make sure to configure the format of the output, in such a way that it can be edited using Microsoft Word. Make sure to put some comments to some of the important parts of the Matlab Program.