Let’s assume we are trying to solve the following differential equation:
As it’s a simple, linear ODE, it can be solved by using as ansatz
If we replace by it, we get
As is nonzero, lambda must be a root of the characteristic polynomial,
Using the well-known “quadratic formula”,
If we call the two values of and , assuming they are different, the general solution will be a linear combination:
If we take the following specific values for the parameters,
(assuming appropriate units)
(assuming appropriate units),
we get the following values for :
Now we have to use the given boundary conditions:
Then the full solution will be:
This solution will quickly diverge for values of not much smaller than one.
Even if the initial conditions were finely tuned for getting , any small numerical error would give a quickly diverging solution.