and are continuous functions of
Is anyone familiar with a possible method to solve such a system (or some kind of perturbation to approx the solution)?
The system can be written in Matrix form as
So as a matrix equation this gives
From here try to Diagonalize the matrix, if that is not possible use the Jordan canonical form. So now we have a matrix that gives
So make the substitution
This gives
and now multiply by P to get
If the matrix was diagonalizable, this will uncouple the linear system into two ODEs. If you could only find JCF then the system will look like
So you have solve for and sub that into the first equation