(1 point)
Use the Laplace transform to solve the following initial value problem: $y'' - 9y' + 20y = 0$, $y(0) = 2$, $y'(0) = 1$
(1) First, using Y for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L}(y(t))$,
find the equation you get by taking the Laplace transform of the differential equation to obtain
$= 0$
(2) Next solve for $Y = $
(3) Now write the above answer in its partial fraction form, $Y = \frac{A}{s - a} + \frac{B}{s - b}$
(NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to $a$ and the second to $b$, where
$a < b$. Also note, for example that $-2 < 1$)
$Y = $
(4) Finally apply the inverse Laplace transform to find $y(t)$
$y(t) = $
