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Differential Equations

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Moderate

Solutions that Oscillate as $t\rightarrow\infty$

DIFFEQ-NVYHCE

Consider the linear system:

$$\begin{eqnarray*}u_1&=u_1+u_2\\\ \\\ u_2&=au_1+u_2\end{eqnarray*}$$

For what values of $a$ does this system have solutions that oscillate as $t\rightarrow\infty$?

A

All real numbers $a$

B

All $a>0$

C

All $a\neq 0$

D

All $a<0$.