1. homogeneous ODE

Anyone have any idea on how to work this question?

Find the general solution of the homogeneous ODE
$\frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0$

2. Originally Posted by mongmong
Anyone have any idea on how to work this question?

Find the general solution of the homogeneous ODE
$\frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0$

3. Originally Posted by mongmong
Anyone have any idea on how to work this question?

Find the general solution of the homogeneous ODE
$\frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0$
The Characteristic Equation is

$m^2 + 2m + 5 = 0$

You should find that in this case the solutions to the Characteristic Equation, $m_1 = a + ib, m_2 = a - ib$ are complex conjugates.
So the solution to your DE will be of the form

$u(t) = Ae^{at}\cos{(b t)} + Be^{at}\sin{(b t)}$

Hopefully you can go from here.