How can I prove this function is a periodic phenomenom?
I´ve been stuck with this math problem for a while and I would really appreciate it if someone could help me with this problem. Any tips or suggestions is fine, I would be really thankful.
So I´ve this differential equation here:
Then I know that if the discriminant of the characteristic equation is negative, it´ll give me two complex solutions and it´ll describe a periodic phenomenon.
I´ve to prove that it´s the case with this equation:
But I really don´t know how to start this? I´ve a general idea that if I get a two complex roots then I can find the modulus of the complex number, theta and also a point cos (x) and sin (y) on the plane. But how do I really prove this to be the case mathematically?