lairaut,s Differential Equation

(1)

or

(2)

where  is a function of one variable and . The general solution is

(3)

The singular solution envelopes are.

A partial differential equation known as Clairaut's equation is given by

(4)

(Iyanaga and Kawada 1980, p. 1446; Zwillinger 1997, p. 132).

REFERENCES:

Boyer, C. B. A History of Mathematics. New York: Wiley, p. 494, 1968.

Ford, L. R. Differential Equations. New York: McGraw-Hill, p. 16, 1955.

Ince, E. L. Ordinary Differential Equations. New York: Dover, pp. 39-40, 1956.

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1446, 1980.

Zwillinger, D. "Clairaut's Equation." §II.A.38 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 120 and 158-160, 1997.