The general solution to the second-order differential equation $\displaystyle \frac{d^2 y}{dt^2} - 2 \frac{dy}{dt} + 8 y = 0$ is in the form $\displaystyle y(x) = e^{\alpha x}\left(c_1 \cos \beta x + c_2 \sin \beta x \right).$ Find the values of $\alpha$ and $\beta,$ where $\beta > 0.$

Answer: $\alpha =$ and $\beta =$