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In this paper, we discuss differentiation of solutions to the boundary valueproblem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\;y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and$y^{(i)}(x_k) + \int_c^d p y(x)\;dx = y_{ik}, \;0 \leq i \leqm_k,\;\sum_{i=1}^km_i=n$ with respect to the boundary data. We show that undercertain conditions, partial derivatives of the solution $y(x)$ of the boundaryvalue problem with respect to the various boundary data exist and solve theassociated variational equation along $y(x)$.

Solutions of the Variational Equation for an nth Order Boundary Value Problem with an Integral Boundary Condition