Exercise 15

Many differential equations have solutions of the form $y(t) = e^{at}$, where $a$ is some constant. For example, $y(t) = e^{3t}$ is a solution to the equation $y' = 3y$. Find all values of $a$ such that $y(t) = e^{at}$ is a solution to the given equation in Finding Solutions.

$y^{(5)} - 5y''' + 4y' = 0$