Hello, I'm trying to solve a differential equation with boundary conditions which leads me to an infinite system of linear equations. I can obtain an approximate solution of the problem just by considering only the first n terms so I have a system of n equations with n unknowns. I've been trying to find an exact solution of the problem by other methods but I always failed, and I suspect that the boundary conditions are incompatible so the exact solution does not exist and that's what I'm trying to prove now. I noticed that the condition number of the system (computationally calculated of course) increases as n increases and that could be a prove that when n is infinite so is the condition number and therefore the matrix is singular. However I don't know how to prove this mathematically, I only can calculate the variation of the contidion number with n for n from 5 to 300 or maybe 400, no more. Does anyone have some ideas to help me??? Thank you so much in advance!!