For a nonzero constant prove that
is a particular solution of the differential equation
Find the general solution of the equation
Proof. The general solution of is
. So, we have particular solutions given by
and
(taking
and
, respectively). The Wronskian of
and
is
So, we have the functions and
of Theorem 8.9 given by
This means we have a particular solution of the non-homogeneous equation given by
Using this theorem we can compute the general solution of
We have