In this problem you will derive the formula for the Laplace transform of the second derivative of a function $y$. Use $y$ and $y^\prime$ for $y(t)$ and $y^\prime (t)$, $y0$ and $y1$ for the initial conditions $y(0)$ and $y^\prime(0)$, and $Y$ for the Laplace transform of $y$.

$\displaystyle L\lbrace y^{\prime\prime}(t)\rbrace(s)=\int_0^\infty e^{-st}y^{\prime\prime}(t) dt$

$\displaystyle u =$ $dv =$

$\displaystyle du =$ $v =$

$\displaystyle =$ $\Bigg\vert_0^\infty + \displaystyle\int_0^\infty$

$\displaystyle =$