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Putnam 1963 A3

Source: Putnam 1963

May 1, 2022
Putnamcalculusintegrationfunctiondifferential equation

Problem Statement

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