Find the general solution of the differential equation
$y''+2y'+2y=0$
The characteristic equation of the given equation is:
$r^2+2r+2=0$
$r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-2\pm\sqrt{4-8}}{2}=-1\pm{i}$
Then,
$$r_1=-1+i \quad r_2=-1-i$$
Therefore, the general solution of the given differential equation is:
$$y=c_1e^{-t}cost+c_2e^{-t}sint$$
