Abstract
A widely studied equation in singular perturbation theory is the second order linear differential equation whose order is lowered when the small parameter is put equal to zero. We use elementary comparison techniques to sharpen and extend in several ways certain of the standard results concerning the asymptotic correctness of the usual asymptotic expansions for solutions of this equation. Our method seems particularly simple and natural for such problems, since the appropriate comparison functions are easily found and motivated intuitively by interpreting the differential equation as a mathematical model of an oscillatory system (using Newton’s second law of motion).
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