The differential equation (d2y/dx2) + ϕ(x)y = 0 where ϕ(x) is a slowly varying function of x can be solved approximately in terms of trigonometric functions. The solution can be applied to find the critical buckling loads for struts of variable bending rigidity and for uniform struts under the action of varying axial forces. The error in using the approximate formulas for buckling loads is in most cases small, and, for all practical purposes, satisfactory results are obtained.

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