Consider the following initial value problem:
$y'' + 64y = \begin{cases} 2, & 0 \le t \le 8 \\ 0, & t > 8 \end{cases}$
$y(0) = 6, \ y'(0) = 0$
First find the unit-step representation of the forcing function, i.e, the right side of the differential equation.
The forcing function can be written as $au(t - b) + cu(t - d)$ with constants $a, b, c, d$. Enter these numbers:
a = $oxed{}$ b = $oxed{}$ c = $oxed{}$ d = $oxed{}$
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 and solve
$Y(s) = oxed{}$