# Graphic Solution of a Second-Order Differential Equation

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This Demonstration shows the Euler–Cauchy method for approximating the solution of an initial value problem with a second-order differential equation. An example of such an equation is , with derivatives from now on always taken with respect to . This equation can be written as a pair of first-order equations, , .

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Contributed by: Izidor Hafner (January 2014)

Open content licensed under CC BY-NC-SA

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References

[1] V. I. Smirnoff, *Lectures in Higher Mathematics* (in Russian), vol. 2, Moscow: Nauka, 1967 p. 50.

[2] L. Euler, "De Integratione Aequationum Differentialium Per Approximationem," *Institutionum Calculi Integralis Volumen Primum*, 1768. www.math.dartmouth.edu/~euler/docs/originals/E342sec2ch7.pdf.

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