How Do You Solve a Damped Harmonic Oscillator Differential Equation?

[razorfever]

damped harmonic oscillator, urgent help needed!

Homework Statement

for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0

Homework Equations

The Attempt at a Solution

I have no idea where to begin, can anyone point me in the right direction or giv me some sort of outline to follow

 

[Redbelly98]

I would first find k1 and k2. This involves solving the quadratic equation you were given.