Putnam 1963 A3

Find an integral formula for the solution of the differential equation $$\delta (\delta-1)(\delta-2) \cdots(\delta -n +1) y= f(x), \;\; x\geq 1,$$ for $y$ as a function of $f$ satisfying the initial conditions $y(1)=y'(1)=\ldots= y^{(n-1)}(1)=0$ , where $f$ is continuous and $\delta$ is the differential operator $x \frac{d}{dx}.$