Hello everyone

I have been given a question of which i am not sure of how to show:

Observe the following differential equation:

$\displaystyle a_{0}\frac{d^{n}y}{dt^{n}}+a_{1}\frac{d^{n-1}y}{dt^{n-1}}+\dots+a_{n-1}\frac{dy}{dt}+a_{n}y=0$

where $\displaystyle a_{0},\dots,a_{n} \in \mathbb{C}$.

Does the above differential equation always have a real solution, besides $\displaystyle y(t) = 0$?

I my self think that it doesn't always have a real solution beside $\displaystyle y(t) = 0$, but i am not sure how to prove/show that i does not.

Can anyone help?

Kind regards

Krisly