The auxiliary equation arising from the given differential equations is:

A.E.:

So and

We have 2 distinct real roots, so we need to use the first solution from the table above (y = Ae^m₁x + Be^m₂x), but we use i instead of y, and t instead of x.

So

We could have written this as:

or

since we have 2 constants of integration. We would be able to find these constants if we were given some initial conditions.