Anyone have any idea on how to work this question?
Find the general solution of the homogeneous ODE
$\displaystyle \frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0$
The Characteristic Equation is
$\displaystyle m^2 + 2m + 5 = 0$
You should find that in this case the solutions to the Characteristic Equation, $\displaystyle m_1 = a + ib, m_2 = a - ib$ are complex conjugates.
So the solution to your DE will be of the form
$\displaystyle u(t) = Ae^{at}\cos{(b t)} + Be^{at}\sin{(b t)}$
Hopefully you can go from here.