To solve a second order constant coefficient differential equation of the form
we assume a solution of the form
To solve a second order constant coefficient differential vector equation of the form
we assume a solution of the form
Suppose we have an equation
with initial conditions
and
at
Assume a solution of the form
so that
and
Substitute these into the differential equation to get
We can factorise with
to obtain
since if
the initial solutions will not be satisfied, and the exponential factor is not equal to 0 for any finite
so
Hence
We have to fit this solution to the initial conditions.
at
(1)
at
(2)
(1)+(2) gives
then from (1)
