Vector Convolution

Problem

Let $u=(u_0,\dots ,u_{m-1})$ and $v=(v-,\dots ,v_{n-1})$ be vectors of length $m$ and $n$ respectively. The convolution of $u$ and $v$, denoted as $u\ast v$ is a vector of length $m+n-1$ with component $k,0\le k\le m\le n$

Polynomial Multiplication

$3y^{\prime \prime }+5y^{\prime }+y=7x$

find transfer function, poles + zeros, ODE gain/DC gain, impulse/step response, time to reach percentage of final value.