Chapter 10.10, Problem 33AP

Show that the general solution to the initial-value problem

$y^{\left(n\right)}+a_1{y}^{\left(n-1\right)}+\cdots +a_{n}y=f\left(t\right)$,

$y\left(0\right)=0$, $y^{\prime }\left(0\right)=0\text{,}\dots \text{,}{y}^{\left(n-1\right)}\left(0\right)=0$,

is

$y\left(t\right)={\displaystyle {\int }_0^{t}K\left(t-w\right)f\left(w\right)dw}$,

For an appropriate function $K\left(t\right)$ that should be determined.