Find the particular solution for the differential equation $\displaystyle \dfrac{d^2x}{dt^2}-\dfrac{dx}{dt}-20x = 0$ that satisfies the initial conditions $\displaystyle x = 0$, $\displaystyle \dfrac{dx}{dt} = 2$ when $\displaystyle t = 0$.

Substituting $\displaystyle x = Ae^{n_{1}x}+Be^{n_{2}x}$, I got $\displaystyle n = 5$ and $\displaystyle n = -4$, so the general solution is $\displaystyle x = Ae^{5t}+Be^{-4t}.$

What I don't know is how to make use of the initial conditions to find $\displaystyle A$ and $\displaystyle B$.