Exercise 20

Use direct substitution to verify that $y(t)$ is a solution of the given differential equation in Initial Value Problems. Then use the initial conditions to determine the constants $C$ or $c_1$ and $c_2$.

$y'' + 4y' + 13y = 0$, $y(0) = 1$, $y'(0) = 0$, $y(t) = c_1 e^{-2t} \cos 3t + c_2 e^{-2t} \sin 3t$