lairaut,s Differential Equation
المؤلف:
Boyer, C. B
المصدر:
A History of Mathematics. New York: Wiley
الجزء والصفحة:
...
11-6-2018
1971
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.
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