Find the particular solution of the differential equation
satisfying the initial condition and
when
.
This is a second-order linear differential equation of the form
These values of and
give us
. So,
and
. By Theorem 8.7 (pages 326-327 of Apostol) we then have
Then computing the first two derivatives, we have
We then use the initial condition ,
Then, we use the other initial condition, ,
Therefore,