Really Quick Differential Equation question

[Saladsamurai]

!Really Quick Differential Equation question...

Homework Statement

Alright so this is what I have for this problem. As you can see I used -i to find my Eigenvectors...now when I find my solution and plug it back into the original, I am getting the opposite of what I am supposed to get.

Was I supposed to use -t instead of +t in my solution since I used lambda=-i to find it?
Or did I make some stupid algebraic error again?

THanks!

 

[Saladsamurai]

I am thinking I should have used cos(-t) and sin(-t) since I used $-i\Rightarrow \alpha=0\ \beta=-1$

 

[Saladsamurai]

I am thinking I should have used cos(-t) and sin(-t) since I used $-i\Rightarrow \alpha=0\ \beta=-1$

I replaced t with -t and this worked. So I will assume my reason was correct.