I am attempting to show that
, with and is ill-conditioned.
I assumed a solution of the form which (of course) lead me to . Solutions to this equation are and .
Thus, . Now we use the boundary conditions given, leading to
How to go from here? The determinant of the coefficient matrix isn't particularly small, either.
Yes I know the matrix is nonsingular (I mentioned the determinant was non-zero). But I think the problem is to show that a small change in the data (i.e. boundary conditions) changes the solution by much. However, I don't find this to be the case.
... with general solution...
... is unstable and that means that initial condition 'only little different' from other can produce a solution that increases without limits with x...