Hi,

I have the following

$\displaystyle y'' + 2y' +3y = 0$

So the auxilary equation would look like $\displaystyle r^2 +2r +3 = 0$

The solution to this equation is on the form $\displaystyle \frac{-2}{2}\pm \sqrt{\frac{4-12}{2}}$

(1)
which evaluates to $\displaystyle -1 \pm \sqrt{\frac{-8}{2}} \rightarrow \sqrt{-4}$

$\displaystyle = -1\pm2i$

Which gives $\displaystyle Ae^{-t}cos(2t) + Be^{-t}sin(2t)$

but apparently thats incorrect, the answer should be $\displaystyle -1\pm\sqrt{2i}$

whats wrong?

Edit: Damn i just remebered there's a forum for DE's. I can't delete my post

Forgive me