The differential equation is equivalent to . The corresponding auxiliary equation is . This implies that the corresponding solutions are and

Thus, the general solution has the form

However, by Euler's formula, we see that and

Thus,

Letting and , we see that the general solution is

Now,

I don't see how the last step is . I believe it should only be . I may be wrong, though. Anyone can correct me if needed...

Does this make sense?