Find the general solution for $$y''' + 2y'' + 2y' = 0$$
Hi, so I have a question on my work for this higher order ODE.
I took the coefficients and plugged it into the characteristic equation:
$$r^3 + 2r^2 + 2r = 0$$ $$r(r^2 + 2r + 2) = 0$$
Using the quadratic formula, I end up with complex roots:
$$ r = -1 + i, r = -1 - i$$ As well as the real root, $r=0$
Anyways, so this is what I got for the General Solution:
$$y = C_1 + C_2e^{-x}cos(x) + C_3e^{-x}sin(x)$$
I tried checking it, but this ended up becoming terrible. Could someone verify my answer is correct?