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.
Using the language of system theory we can say that adinamic system defined by the DE...
(1)
... with general solution...
(1)
... is unstable and that means that initial condition 'only little different' from other can produce a solution that increases without limits with x...
Kind regards