Clairaut's Difference Equation

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

(1)

or in " notation,"

(2)

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

(3)

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.