Exercise 24

Use direct substitution to verify that $y(t)$ is a solution of the given differential equation in Boundary Value Problems. Then use the boundary conditions to determine the constants $c_1$ and $c_2$ (if possible).

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