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Clairaut's Difference Equation

Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by

u_k=kDeltau_k+F(Deltau_k),
(1)

or in "x notation,"

y=x(Deltay)/(Deltax)+F((Deltay)/(Deltax))
(2)

(Spiegel 1970). It is so named by analogy with Clairaut's differential equation

y=x(dy)/(dx)+F((dy)/(dx)).
(3)

See also

Clairaut's Differential Equation

This entry contributed by Ronald M. Aarts

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References

Sokolnikoff, I. S. and Redheffer, R. M. Mathematics of Physics and Modern Engineering. New York: McGraw-Hill, 1958.Spiegel, M. R. Schaum's Outline of Theory and Problems of Calculus of Finite Differences and Difference Equations. New York: McGraw-Hill, 1970.

Referenced on Wolfram|Alpha

Clairaut's Difference Equation

Cite this as:

Aarts, Ronald M. "Clairaut's Difference Equation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ClairautsDifferenceEquation.html

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