Let us consider the homogeneous linear system of differential
equations
where the aij are known constants and primes denote
derivatives with respect to t.
The system (1) can be written in matrix form as
where
The problem of finding a solution x(t) to (1) such that
, where 
is a given
vector, is called
an initial value problem. In the case of a two point boundary value
problem, instead of initial condition , we
have
